26-Problemas com Valores Absolutos Resolvendo todos os tipos de equa\303\247\303\265es com valor absoluto b\303\241sico.

restart: with(plots):

Warning, the name changecoords has been redefined

PointsPlot := proc( a, b ) #description "plot a finite interval on a number line"; local wid,Axesplot,leftpt,rightpt,leftend,rightend,LT,RT,ZT,textpos,zp; wid := ceil( (b-a)/15) ; textpos := max(wid, 2) ; LT := textplot( [a, textpos, a] ): RT := textplot( [b, textpos, b] ): ZT := textplot( [0, textpos, 0] ): leftend := min( a - 2*wid, 0); rightend := max( b + 2*wid, 0); Axesplot := plot( 0, x = leftend..rightend , y = (-wid)..(2*wid), axes = none, thickness = 4, color = blue, scaling = constrained, tickmarks = [1,1] ): zp := plot( [[0,-wid/3],[0,wid/3]], color = black ); leftpt := plottools[disk]([ a, 0], wid/2, color=red): rightpt := plottools[disk]([ b, 0], wid/2, color=red ): display( [Axesplot, LT, RT, ZT, leftpt, rightpt,zp ]); end proc: intfin := proc( a, b, leq, req ) #description "plot a finite interval on a number line"; local r, M, v1, v2, wid, bar, Axesplot, leftpt, rightpt, pt_color, leftend, rightend, LT, RT, IT, textpos, lt, rt; r := b-a ; M := evalf( 1.2 * max( b-a, abs(a), abs(b) ) ); v1 := [a, 0]; v2 := [b, 0]; wid := ceil( M/15) ; bar := arrow( v1, v2, shape = double_arrow, color = red , difference = certo, width = wid, head_width = 0, head_length = 0): if( leq ) then lt := `[`; else lt := `(`; fi; if( req ) then rt := `]`; else rt := `)`; fi; textpos := max(wid, 2) ; LT := textplot( [a, textpos, a] ): RT := textplot( [b, textpos, b] ): IT := textplot( [(a+b)/2, textpos + wid, cat(lt,a,`,`,b,rt)], color = green ): leftend := min( a - 2*wid, 0); rightend := max( b + 2*wid, 0); Axesplot := plot( 0, x = leftend..rightend , y = (-wid)..(2*wid), axes = none, thickness = 2, scaling = constrained, tickmarks = [1,1] ): if( leq ) then pt_color := red; else pt_color := white; fi; leftpt := plottools[disk]([ a, 0], wid/2, color=pt_color): if( req ) then pt_color := red; else pt_color := white; fi; rightpt := plottools[disk]([ b, 0], wid/2, color=pt_color ): display( leftpt, rightpt, bar, Axesplot, LT, RT, IT ); end proc: #__________________________________________________________ intinfr := proc(a, leq ) # description "plot an infinite interval going to +inf"; local bb, r, M, v1, v2, wid, bar, Axesplot, textpos, leftpt, rightpt, pt_color, leftend, rightend, LT, RT, IT,lt; bb := max( 3*abs(a), 5) ; r := bb-a; M := evalf(1.2* max( abs(r), abs(a))); v1 := [a, 0]; v2 := [bb, 0]; wid := ceil( M/15); bar := arrow( v1, v2, shape = double_arrow, color = red , difference = certo, width = wid, head_width = 1.8*wid, head_length = 1.2*wid): if( leq ) then lt := `[`; else lt := `(`; fi; textpos := max(wid, 3) ; LT := textplot( [a, textpos, a] ): RT := textplot( [bb, textpos, `Infinity`] ): IT := textplot( [(a+bb)/2, textpos + wid, cat(lt,a,`, infinty)`)], color = green ): leftend := min( 0, a*1.5); rightend := max( 0, bb); Axesplot := plot( 0, x = leftend..rightend , y = (-wid)..(3*wid), axes = none, thickness = 2, scaling = constrained, tickmarks = [1,1] ): if( leq ) then pt_color := red; else pt_color := white; fi; leftpt := plottools[disk]([ a, 0], wid/2, color=pt_color): display( leftpt, bar, Axesplot, LT, RT, IT ); end proc: #__________________________________________________________ intinfl := proc( b, req ) # description "plot a infinite interval going to -inf"; local aa, bb, r, M, v1, v2, wid, bar, Axesplot,textpos, leftpt, rightpt, pt_color, leftend, rightend, LT, RT, IT, rt; aa := min( -3*abs(b), -5); r := b-aa; M := evalf(1.2*max( abs(r), abs(b) )); v1 := [aa, 0]; v2 := [b, 0]; wid := ceil( M/15); bar := arrow( v2, v1, shape = double_arrow, color = red , difference = certo, width = wid, head_width = 1.8*wid, head_length = 1.2*wid): textpos := max(wid, 3) ; if( req ) then rt := `]`; else rt := `)`; fi; LT := textplot( [aa, textpos, `-Infinity`] ): RT := textplot( [b, textpos, b] ): IT := textplot( [(aa+b)/2, textpos + wid, cat(`(-infinity,`,b,rt)], color = green ): leftend := min( 0, aa); rightend := max( 0, b*1.5); Axesplot := plot( 0, x = leftend..rightend , y = (-wid)..(3*wid), axes = none, thickness = 2, scaling = constrained, tickmarks = [1,1] ): if( req ) then pt_color := red; else pt_color := white; fi; rightpt := plottools[disk]([ b, 0], wid/2, color=pt_color): display( rightpt, bar, Axesplot, LT, RT , IT); end proc: #__________________________________________________________ intall := proc() #description "plot a infinite interval of all real numbers "; local a, b, v1, v2, wid, bar1, bar2, LT, RT, Axesplot ; a := -25; b := 25; v1 := [a, 0]; v2 := [b, 0]; wid := ceil( (b-a)/15); bar1 := arrow( v1, shape = double_arrow, color = red , difference = falso, width = wid, head_width = 1.8*wid, head_length = 1.2*wid): bar2 := arrow( v2, shape = double_arrow, color = red , difference = falso, width = wid, head_width = 1.8*wid, head_length = 1.2*wid): LT := textplot( [a, max( wid, 6), `Infinity`] ): RT := textplot( [b, max( wid, 6), `Infinity`] ): Axesplot := plot( 0, x = a..b , y = (-wid)..(3*wid), axes = none, thickness = 2, scaling = constrained, tickmarks = [1,1] ): display( bar1, bar2, Axesplot, LT, RT ); end proc: #__________________________________________________________ #__________________________________________________________ intv := proc( expr1, expr2 ) # description "plot a infinite interval going to -inf"; local a, b, leq, req; if type( expr1, `<=`) then leq := verdadeiro; else leq := falso; fi; if type( expr2, `<=`) then req := verdadeiro; else req := falso; fi; a := lhs( expr1); b := rhs( expr2); if( abs(a) <> infinity) then if( abs(b) <> infinity) then intfin( a,b, leq, req ); else intinfr( a, leq); fi; else if( abs(b) <> infinity) then intinfl( b, req); else intall(); fi; fi; end proc:

Existe uma dualidade em valores absolutos.Quando temos uma equa\303\247\303\243o simples como |x| = 12, temos duas respostas poss\303\255veis: +12 porque |12| = 12, e -12 porque |-12| = 12. abs(x) = 12; x = {solve(%,x)};

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PointsPlot( -12, 12 );

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Quando tentamos solucionar esse tipo de equa\303\247\303\243o, dividimos a equa\303\247\303\243o em duas equa\303\247\303\265es lineares sem valores absolutos. x = 12; solve(%); x = -12; solve(%);

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Sempre que tivermos uma equa\303\247\303\243o |x| = a (a >0), as solu\303\247\303\265es ser\303\243o dois pontos, simetricamente posicionados a partir da origem. abs(x) = 7; x = {solve(%,x)}; PointsPlot( -7,7 );

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Mais exemplos - isso funciona da mesma forma. No entanto, j\303\241 que -0 = 0, s\303\263 h\303\241 uma resposta para |x| = 0. E j\303\241 que |x| >= 0, n\303\243o temos solu\303\247\303\243o tendo um valor n\303\243o negativo igualado a um valor negativo. abs(x) = 100; x = {solve(%,x)};

NiMvLSUkYWJzRzYjJSJ4RyIkKyI=NiMvJSJ4RzwkISQrIiIkKyI=

abs(x) = 2; x = {solve(%,x)};

NiMvLSUkYWJzRzYjJSJ4RyIiIw==NiMvJSJ4RzwkISIjIiIj

abs(x) = 0; x = {solve(%,x)};

NiMvLSUkYWJzRzYjJSJ4RyIiIQ==NiMvJSJ4RzwjIiIh

abs(x) = -5; x = {solve(%,x)};

NiMvLSUkYWJzRzYjJSJ4RyEiJg==NiMvJSJ4Rzwi

\303\211 um pouco mais complicado quando n\303\243o estamos lidando com apenas |x| e sim o valor absoluto de uma express\303\243o linear de x. abs(x - 3) = 10; x = {solve(%,x)};

NiMvLSUkYWJzRzYjLCYlInhHIiIiIiIkISIiIiM1NiMvJSJ4RzwkISIoIiM4

Como antes, a maneira de resolver isso a m\303\243o \303\251 dividir em duas equa\303\247\303\265es lineares diferentes. (x-3) = 10; solve(%); (x-3) = -10; solve(%);

NiMvLCYlInhHIiIiIiIkISIiIiM1NiMiIzg=NiMvLCYlInhHIiIiIiIkISIiISM1NiMhIig=

quando a express\303\243o do valor absoluto \303\251 mais complicada , as solu\303\247\303\265es n\303\243o s\303\243o mais sim\303\251tricas. PointsPlot( -7, 13);

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Veja outros exemplos. abs( 8*x + 3 ) = 13; x = {solve(%,x)}; ( 8*x + 3 ) = 13; x = {solve(%,x)}; ( 8*x + 3 ) = -13; x = {solve(%,x)}; PointsPlot( -2, 5/4 );

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abs( 5*x - 9) = 16; x = {solve(%,x)}; ( 5*x - 9 ) = 16; x = {solve(%,x)}; ( 5*x - 9) = -16; x = {solve(%,x)}; PointsPlot( -7/5, 5 );

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Quando consideramos uma inequa\303\247\303\243o da forma | x | < 3, estamos olhando a todos os n\303\272meros positivos menores ou iguais a 3, e seus negativos. Vamos ver os inteiros que satifazem essa inequa\303\247\303\243o. (\303\251 claro que estamos vendo todo os n\303\272meros reais que a satisfazem, mas isso \303\251 s\303\263 para nos dar umas pistas.) for k from -8 to 8 do k, evalb( abs(k) <= 3 ); od;

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Como pode ver, os \303\272nicos valores que satisfazem | x | < 3 s\303\243o -3, -2, -1, 0, 1, 2, e 3. Para resolver esse tipo de equa\303\247\303\243o a m\303\243o, geralmente fazemos uma inequa\303\247\303\243o de tr\303\252s lados: -3 < x < 3. Apesar de n\303\243o podermos fazer isso no Maple, podemos resolver cada uma separadamente e aceitar a interse\303\247\303\243o como resposta. abs( x ) <= 3; -3, `<`, x, `<`, 3;

NiMxLSUkYWJzRzYjJSJ4RyIiJA==NichIiQlIjxHJSJ4R0YkIiIk

-3 <= x; N := solve(%); x <= 3; P := solve(%); N intersect P; solve( abs(x) <= 3, x);

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Este \303\251 o gr\303\241fico da solu\303\247\303\243o. intv( -3 <= x, x <= 3 );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

Este \303\251 outro exemplo onde a resposta \303\251 o intervalo aberto. abs( x ) < 10; solve(%); intv( -10 < x, x < 10);

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Vamos agora inverter a vis\303\243o e examinar o caso onde o valor absoluto \303\251 maior ou igual que um n\303\272mero. Para ter uma id\303\251ia do que est\303\241 havendo, vamos investigar quais inteiros satisfazem essa inequa\303\247\303\243o. for k from -8 to 8 do k, evalb( abs(k) >= 3 ); od;

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Como podemos ver, essa lista \303\251 bem diferente da lista que vimos na se\303\247\303\243o anterior. \303\211 quase oposta, na verdade. Todos os n\303\272meros que antes eram verdadeiros agora s\303\243o falsos e vice versa, exceto por 3 e -3 que s\303\243o verdadeiros em ambos os casos. O que podemos ver nessa lista \303\251 que a solu\303\247\303\243o para esse tipo de inequa\303\247\303\243o consiste em dois grupos separados de n\303\272meros - os 'grandes' n\303\272meros positivos maiores ou iguais a 3 e seu negativos. Esses dois conjuntos de n\303\272meros s\303\243o distintos , j\303\241 que os n\303\272meros entre -3 e 3 n\303\243o satisfazem a inequa\303\247\303\243o. Isso nos diz que a solu\303\247\303\243o vai incluir duas inequa\303\247\303\265es separadas. abs( x ) >= 3; x >= 3, x <= -3;

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abs( x ) >= 3; solve(%);

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display( intv( 3 <= x, x < infinity ), intv( -infinity < x, x <= -3 ) );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

Observe a conex\303\243o entre as inequa\303\247\303\265es e suas solu\303\247\303\265es: |x| < 3 a solu\303\247\303\243o \303\251 [-3,3] |x| > 3 a solu\303\247\303\243o \303\251 a uni\303\243o 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 Juntos, esses dois conjuntos cobrem a linha num\303\251rica INTEIRA. Eles s\303\243o como partes interligadas de um quebra-cabe\303\247a. display( intv( -3 <= x, x < 3 ) ); display( intv( 3 <= x, x < infinity ), intv( -infinity < x, x <= -3 ) );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

Este \303\251 outro exemplo. Novamente os intervalos s\303\243o sim\303\251tricos nesse tipo mais simples de problema. abs(x) > 15 ; solve(%); display( intv( 15 < x, x < infinity ), intv( -infinity < x, x < -15 ) );

NiMyIiM6LSUkYWJzRzYjJSJ4Rw==NiQtJSpSZWFsUmFuZ2VHNiQtJSVPcGVuRzYjIiM6JSlpbmZpbml0eUctRiQ2JCwkRiohIiItRic2IyEjOg==Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

Tamb\303\251m podemos aplicar esses princ\303\255pios para valores absolutos mais complicados. \303\211 importante ficar clara a diferen\303\247a b\303\241sica entre valores absolutos menores que e maiores que n\303\272meros. | x | < a or 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 .... solucionada por uma inequa\303\247\303\243o de tr\303\252s lados | x | > a or 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 .... solucionada por duas inequa\303\247\303\265es essas duas distin\303\247\303\265es se aplicam a casos mais complicados. | ax+b | < c or 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 .... solucionada por uma inequa\303\247\303\243o de tr\303\252s lados | ax+b | > c or 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 .... solucionada por duas inequa\303\247\303\265es abs( 5*x + 2) < 17; -17, `<`, 5*x + 2, `<`, 17; -19, `<`, 5*x , `<`, 15; -19/5, `<`, x , `<`, 15/5;

NiMyLSUkYWJzRzYjLCYqJiIiJiIiIiUieEciIiIiIiIiIiMiIiIiIzw=NichIzwlIjxHLCYqJiIiJiIiIiUieEdGKEYoIiIjRihGJCIjPA==NichIz4lIjxHLCQqJiIiJiIiIiUieEdGKEYoRiQiIzo=NicjISM+IiImJSI8RyUieEdGJiIiJA==

abs( 5*x + 2) < 17; solve(%);

NiMyLSUkYWJzRzYjLCYqJiIiJiIiIiUieEciIiIiIiIiIiMiIiIiIzw=NiMtJSpSZWFsUmFuZ2VHNiQtJSVPcGVuRzYjIyEjPiIiJi0lJU9wZW5HNiMiIiQ=

display( intv( 3 < x, x < infinity ), intv( -infinity < x, x < - 19/5 ) );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

abs( 3*x - 8) <= 7; solve(%);

NiMxLSUkYWJzRzYjLCYqJiIiJCIiIiUieEciIiIiIiIiIikhIiIiIig=NiMtJSpSZWFsUmFuZ2VHNiQjIiIiIiIkIiIm

display( intv( 4/3 < x, x < infinity ), intv( -infinity < x, x < -1 ) );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

Tamb\303\251m podemos aplicar esses princ\303\255pios a valores absolutos mais complicados que sejam maiores que ou maiores que ou iguais. | x | > a or 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 .... solucionada por duas inequa\303\247\303\265es | ax+b | > c or 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 .... solucionada por duas inequa\303\247\303\265es abs( 3*x + 2) > 7; solve(%);

NiMyIiIoLSUkYWJzRzYjLCYqJiIiJCIiIiUieEciIiIiIiIiIiMiIiI=NiQtJSpSZWFsUmFuZ2VHNiQtJSVPcGVuRzYjIyIiJiIiJCUpaW5maW5pdHlHLUYkNiQsJEYsISIiLUYnNiMhIiQ=

display( intv( 5/3 < x, x < infinity ), intv( -infinity < x, x < -3 ) );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

abs( 6*x - 1) >= 7; solve(%);

NiMxIiIoLSUkYWJzRzYjLCYqJiIiJyIiIiUieEciIiIiIiIiIiIhIiI=NiQtJSpSZWFsUmFuZ2VHNiQjIiIlIiIkJSlpbmZpbml0eUctRiQ2JCwkRikhIiJGLQ==

display( intv( 4/3 < x, x < infinity ), intv( -infinity < x, x < -1 ) );

Error, (in ProcessOptions) argument 'difference = certo' invalid: rhs should be of type truefalse

Voc\303\252 pode visualizar o valor absoluto de uma equa\303\247\303\243o ao observar a interse\303\247\303\243o de dois gr\303\241ficos. . abs( x ) = 3; solve( %); plot( {lhs(%%), rhs(%%)}, x = -5..5, thickness = 2); `Note que dois pontos da interse\303\247\303\243o signifca as duas solu\303\247\303\265es da equa\303\247\303\243o`;

NiMvLSUkYWJzRzYjJSJ4RyIiJA==NiQiIiQhIiQ=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

abs( x ) = 0; solve( %); plot( {lhs(%%), rhs(%%)}, x = -5..5, thickness = 2); `Note que UM ponto de interse\303\247\303\243o significa UMA solu\303\247\303\243o para a equa\303\247\303\243o`;

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b250b35kZX5pbnRlcnNlfGp5fGp2fGh2fGp5fGp2fGh2b35zaWduaWZpY2F+VU1BfnNvbHV8anl8anZ8aHZ8anl8anZ8aHZvfnBhcmF+YX5lcXVhfGp5fGp2fGh2fGp5fGp2fGh2Rw==

abs(x) = -4; solve( %); plot( {abs(x), -4}, x = -5..5, thickness = 2); `Note que nenhum ponto da interse\303\247\303\243o significa sem solu\303\247\303\243o para a equa\303\247\303\243o`;

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dG9+ZGF+aW50ZXJzZXxqeXxqdnxodnxqeXxqdnxodm9+c2lnbmlmaWNhfnNlbX5zb2x1fGp5fGp2fGh2fGp5fGp2fGh2b35wYXJhfmF+ZXF1YXxqeXxqdnxodnxqeXxqdnxodkc=

Aqui temos exemplos de casos mais complicados. abs( 2*x + 7) = 12; solve( %); plot( {lhs(%%), rhs(%%)}, x = -12..5, thickness = 2);

NiMvLSUkYWJzRzYjLCYqJiIiIyIiIiUieEciIiIiIiIiIigiIiIiIzc=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NiI=

abs( 7*x - 3) = 11; solve( %); plot( {lhs(%%), rhs(%%)}, x = -5..7, thickness = 2);

NiMvLSUkYWJzRzYjLCYqJiIiKCIiIiUieEciIiIiIiIiIiQhIiIiIzY=NiQiIiMjISIpIiIoNiwtJSdDVVJWRVNHNiQ3UzckJCEjXSEiIiQiJDUiISIiNyQkISo6TSVRWiEiKSQiJDUiISIiNyQkISxENVozXiUhIzUkIiQ1IiEiIjckJCErbDshXEQlISIqJCIkNSIhIiI3JCQhMigqKioqKlxsZnMqUiEjOyQiJDUiISIiNyQkISxEPFUzdSQhIzUkIiQ1IiEiIjckJCEyLisrRE01Sl0kISM7JCIkNSIhIiI3JCQhLEQhRyZwRCQhIzUkIiQ1IiEiIjckJCEsREt3QiskISM1JCIkNSIhIiI3JCQhLERGOydbRiEjNSQiJDUiISIiNyQkISooR2YoWyMhIikkIiQ1IiEiIjckJCErOkxvZEEhIiokIiQ1IiEiIjckJCEyKSoqKioqKjQnZikpKj4hIzskIiQ1IiEiIjckJCEqOnQqUTwhIikkIiQ1IiEiIjckJCEyKSoqKioqKipRQyYpWyIhIzskIiQ1IiEiIjckJCEsRCNINGg3ISM1JCIkNSIhIiI3JCQhMSoqKioqKio0XGwhKiohIzskIiQ1IiEiIjckJCEpV2U6dyEiKSQiJDUiISIiNyQkITEsKytEeWtdXCEjOyQiJDUiISIiNyQkITJOKysrU0Y8ZiMhIzwkIiQ1IiEiIjckJCEwVCgqKioqXCN5aCQhIz0kIiQ1IiEiIjckJCIxLisrRFgoM1kjISM7JCIkNSIhIiI3JCQiMS8rK11QSktdISM7JCIkNSIhIiI3JCQiMS8rK3Z3cCRSKCEjOyQiJDUiISIiNyQkIjEqKioqKipcI3AyJSoqISM7JCIkNSIhIiI3JCQiLHYyWSdlNyEjNSQiJDUiISIiNyQkIjIpKioqKlwtViYqKVsiISM7JCIkNSIhIiI3JCQiMi4rK11cJHBQPCEjOyQiJDUiISIiNyQkIjInKioqKioqPmFtJSo+ISM7JCIkNSIhIiI3JCQiMicqKioqKlxKaWdDIyEjOyQiJDUiISIiNyQkIix2dCwkKlsjISM1JCIkNSIhIiI3JCQiK1h3UGZGISIqJCIkNSIhIiI3JCQiMSoqKioqKmZHMC1JISM6JCIkNSIhIiI3JCQiKlhnNkUkISIpJCIkNSIhIiI3JCQiMiYqKioqXFAvJmZcJCEjOyQiJDUiISIiNyQkIjIyKysrInpqX1AhIzskIiQ1IiEiIjckJCIxKioqKlw8MzslKlIhIzokIiQ1IiEiIjckJCIsdiU9aVlVISM1JCIkNSIhIiI3JCQiMiYqKioqKipcJ1tNXCUhIzskIiQ1IiEiIjckJCIxKioqKlxQTSY9diUhIzokIiQ1IiEiIjckJCIxLCsrZ3pzK10hIzokIiQ1IiEiIjckJCIrMCJRX0QmISIqJCIkNSIhIiI3JCQiMSwrXXgyazJiISM6JCIkNSIhIiI3JCQiMSwrKz9FZFJkISM6JCIkNSIhIiI3JCQiKyZvI1IwZyEiKiQiJDUiISIiNyQkIipLWEpDJyEiKSQiJDUiISIiNyQkIix2QFJtXCchIzUkIiQ1IiEiIjckJCIsREFsI1JuISM1JCIkNSIhIiI3JCQiI3EhIiIkIiQ1IiEiIi0lJkNPTE9SRzYmJSRSR0JHJCIjNSEiIiQiIiEhIiIkIiIhISIiLSUnQ1VSVkVTRzYkN2ZuNyQkISNdISIiJCIkIVEhIiI3JCQhKjpNJVFaISIpJCIyJioqKioqXCFSIXBoJCEjOjckJCEsRDVaM14lISM1JCIyJyoqKlw8KEhmZE0hIzo3JCQhK2w7IVxEJSEiKiQiLGI7SiV5SyEiKjckJCEyKCoqKioqXGxmcypSISM7JCIyKCoqKipcZTwzKTQkISM6NyQkISxEPFUzdSQhIzUkIi12PyYqZT1IISM1NyQkITIuKytETTVKXSQhIzskIi12UnM8X0YhIzU3JCQhLEQhRyZwRCQhIzUkIi12aHAnKXpEISM1NyQkISxES3dCKyQhIzUkIi12RE1tLEMhIzU3JCQhLERGOydbRiEjNSQiLXYhUkpTQSMhIzU3JCQhKihHZihbIyEiKSQiKzRdSlQ/ISIpNyQkISs6TG9kQSEiKiQiMi0rKzBLeS4pPSEjOjckJCEyKSoqKioqKjQnZikpKj4hIzskIjIpKioqKipwcywjKnAiISM6NyQkISo6dCpRPCEiKSQiMiwrK10/Ikc8OiEjOjckJCEyKSoqKioqKipRQyYpWyIhIzskIjIpKioqKipIMm4+TSIhIzo3JCQhLEQjSDRoNyEjNSQiLXZYXXcjPSIhIzU3JCQhMSoqKioqKio0XGwhKiohIzskIipQJWVNKiohIik3JCQhKVdlOnchIikkIiozNDRMKSEiKTckJCExLCsrRHlrXVwhIzskIjIwKyt2WmBhWSchIzs3JCQhMk4rKytTRjxmIyEjPCQiMS0rKyE9NFUiWyEjOjckJCEwVCgqKioqXCN5aCQhIz0kIjEpKioqXHhDYC1JISM6NyQkIjJHKysrTkcnRzchIzwkIjEpKioqKlw6ZypSQCEjOjckJCIxLisrRFgoM1kjISM7JCIyeioqKlxLeVF4NyEjOzckJCIxLitESlZ0LkohIzskIjF2Klw3b2ZRRikhIzs3JCQiMk0rK3Y4JWZZUCEjPCQiMmwoKipcUDUlUXgkISM8NyQkIjJNXWkhKjM0dCFSISM8JCIyY1ppbFBPKVtFISM8NyQkIjJNK0QxL0Mhb1MhIzwkIjJbKFxpOjwkUV8iISM8NyQkIjJOXSg9IyoqUShHVSEjPCQiMVJaKG9hcSMpKVIhIzw3JCQiMk4rXVAlUlgqUSUhIzwkIjFELV1pZ3hocyEjPDckJCIyTyt2byVRKTNyJSEjPCQiMUNdN0dwPXdIISM7NyQkIjEvKytdUEpLXSEjOyQiMUUrK11pPkVfISM7NyQkIjEvK103ZCs4aSEjOyQiMS4rdikqUjVcOCEjOjckJCIxLysrdndwJFIoISM7JCIyRisrRFApZXZAISM7NyQkIjEqKioqKipcI3AyJSoqISM7JCIyIyoqKioqXFpRJmVSISM7NyQkIix2MlknZTchIzUkIjEqKioqXFVEXzVlISM6NyQkIjIpKioqKlwtViYqKVsiISM7JCIxKioqKlw8LG9BdSEjOjckJCIyLisrXVwkcFA8ISM7JCIxLSsrbFcmUTsqISM6NyQkIjInKioqKioqPmFtJSo+ISM7JCIyJyoqKioqUnpsaTQiISM6NyQkIjInKioqKipcSmlnQyMhIzskIjIoKioqKlw/T0NzNyEjOjckJCIsdnQsJCpbIyEjNSQiLUQ7N15VOSEjNTckJCIrWHdQZkYhIiokIjIpKioqKlxeVmNKOyEjOjckJCIxKioqKioqZkcwLUkhIzokIjIlKioqKio+K1A5IT0hIzo3JCQiKlhnNkUkISIpJCIyLisrXUo3Ryk+ISM6NyQkIjImKioqKlxQLyZmXCQhIzskIjInKioqXGlJbHI5IyEjOjckJCIyMisrKyJ6al9QISM7JCIyMCsrcWBZb0sjISM6NyQkIjEqKioqXDwzOyUqUiEjOiQiMiUqKipcQWQ3ZlwjISM6NyQkIix2JT1pWVUhIzUkIi1EJEhORW4jISM1NyQkIjImKioqKioqXCdbTVwlISM7JCIyKSoqKioqXDA5YSVHISM6NyQkIjEqKioqXFBNJj12JSEjOiQiMiQqKipcaVMoSEVJISM6NyQkIjEsKytnenMrXSEjOiQiMSwrK3MmNDA/JCEjOTckJCIrMCJRX0QmISIqJCIsTm5tJ3lMISIqNyQkIjEsK114MmsyYiEjOiQiMjArXVVhW2BiJCEjOjckJCIxLCsrP0VkUmQhIzokIitNM3E8UCEiKTckJCIrJm8jUjBnISIqJCIsJnpbeC5SISIqNyQkIipLWEpDJyEiKSQiK0M8P3FTISIpNyQkIix2QFJtXCchIzUkIi1EX3VrWlUhIzU3JCQiLERBbCNSbiEjNSQiLXZiY1s8VyEjNTckJCIjcSEiIiQiJGclISIiLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIjNSEiIiQiIiEhIiItJSVWSUVXRzYkOyQhI10hIiIkIiNxISIiJShERUZBVUxURy0mJSZfQVhJU0c2IyIiIjYnLSUrX0dSSURMSU5FU0c2Jy0lJkNPTE9SRzYmJSRSR0JHJCIiISEiIiQiIiEhIiIkIiIhISIiLSUqTElORVNUWUxFRzYjIiIhLSUqVEhJQ0tORVNTRzYjIiIhLSUtVFJBTlNQQVJFTkNZRzYjJCIiISEiIi0lKV9WSVNJQkxFRzYjIiIhLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSYlJl9BWElTRzYjIiIjNictJStfR1JJRExJTkVTRzYnLSUmQ09MT1JHNiYlJFJHQkckIiIhISIiJCIiISEiIiQiIiEhIiItJSpMSU5FU1RZTEVHNiMiIiEtJSpUSElDS05FU1NHNiMiIiEtJS1UUkFOU1BBUkVOQ1lHNiMkIiIhISIiLSUpX1ZJU0lCTEVHNiMiIiEtJSZDT0xPUkc2JiUkUkdCRyQiIiEhIiIkIiIhISIiJCIiISEiIi0lKkxJTkVTVFlMRUc2IyIiIS0lKlRISUNLTkVTU0c2IyIiIS0lLVRSQU5TUEFSRU5DWUc2IyQiIiEhIiItJStBWEVTTEFCRUxTRzYkUSJ4NiJRITYiLSUqVEhJQ0tORVNTRzYjIiIjLSUpX1ZJU0lCTEVHNiMiIiItJSVST09URzYnLSUpQk9VTkRTX1hHNiMkIiMhKSEiIi0lKUJPVU5EU19ZRzYjJCIjcSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJSFmJCEiIi0lLkJPVU5EU19IRUlHSFRHNiMkIiVTSyEiIi0lKUNISUxEUkVORzYiLSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZRzYjJCIiISEiIi0lLUJPVU5EU19XSURUSEc2IyQiJStTISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJStTISIiLSUpQ0hJTERSRU5HNiI=NiI=

E quanto a inequa\303\247\303\265es no lugar das equa\303\247\303\265es? As igualdades mostram onde s\303\243o os pontos de interse\303\247\303\243o. abs( 2*x - 7) = 9; solve( %); plot( {lhs(%%), rhs(%%)}, x = -4..12, thickness = 2);

NiMvLSUkYWJzRzYjLCYqJiIiIyIiIiUieEciIiIiIiIiIighIiIiIio=NiQiIikhIiI=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

Quando o valor absoluto \303\251 MENOR que a constante, ent\303\243o temos que procurar pelo V ABAIXO da linha horizontal. display( plot( { abs( 2*x - 7), 9 }, x = -5..12, thickness = 2), polygonplot( { [[8,9], [-1,9], [3.5,0]] } , color = blue ) ); abs( 2*x - 7) < 9;

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SyEiIi0lKUNISUxEUkVORzYiLSUrQU5OT1RBVElPTkc2Jy0lKUJPVU5EU19YRzYjJCIiISEiIi0lKUJPVU5EU19ZRzYjJCIiISEiIi0lLUJPVU5EU19XSURUSEc2IyQiJStTISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJStTISIiLSUpQ0hJTERSRU5HNiI=NiI=NiMyLSUkYWJzRzYjLCYqJiIiIyIiIiUieEciIiIiIiIiIighIiIiIio=

Quando o valor absoluto \303\251 MAIOR que a constante, temos ent\303\243o que encontrar o V ACIMA da linha horizontal. display( plot( { abs( 2*x - 7), 9 }, x = -5..12, thickness = 2), polygonplot( { [[8,9], [12,9], [12,17]], [[-1,9], [-5,9], [-5,17]] } , color = blue ) ); abs( 2*x - 7) > 9;

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JCIjcSEiIi0lLUJPVU5EU19XSURUSEc2IyQiJVNOISIiLSUuQk9VTkRTX0hFSUdIVEc2IyQiJVNLISIiLSUpQ0hJTERSRU5HNiItJStBTk5PVEFUSU9ORzYnLSUpQk9VTkRTX1hHNiMkIiIhISIiLSUpQk9VTkRTX1lHNiMkIiIhISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlK1MhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlK1MhIiItJSlDSElMRFJFTkc2Ig==Ig==NiMyIiIqLSUkYWJzRzYjLCYqJiIiIyIiIiUieEciIiIiIiIiIighIiI=