EXERCÍCIOS DA UNIDADE I MÓDULO 7

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EXERCÍCIOS DA UNIDADE I MÓDULO 7
I) Complete:
1) A expressão escrita à esquerda do sinal de igualdade chama-se PRIMEIRO MEMBRO
2) A expressão escrita à direita do sinal de igualdade chama-se SEGUNDO MEMBRO
3) Em uma equação de 1o grau, a variável aparece com o expoente UM
4) quando você substitui uma variável por um número, tornando verdadeira a sentença, você está achando a SOLUÇÃO ou A RAIZ da equação.
5) Quando uma equação não tem raiz, dizemos que o conjunto-solução é VAZIO
II) Escreva nos parênteses S (sim) ou N (não) para indicar se o valor dado à variável é raiz da equação.
1) ( S ) 9x + 1 = 10, sendo x = 1 
 9.1 + 1 = 10 9 + 1 = 10 10 = 10 verdade
2) ( S ) 7z + 1 = 5z + 3, para z =1 
 7.1 + 1 = 5.1 + 3 7 + 1 = 5 + 3 8 = 8 verdade
3) ( S ) 4u – 5 = 3(u – 1), para u = 2 
 4.2 – 5 = 3 (2 – 1) 8 – 5 = 3. 1 3 = 3 verdade
4) ( S ) 14 – x = x, sendo x = 7 
 14 – 7 = 7 7 = 7 verdade
5) ( N ) x/2 + 3 = 6, para x = 4 
 4:2 + 3 = 6 2 + 3 = 6 5 = 6 falso 
6) ( N ) 8x = 2(3x – 1) – 16, sendo = 1 
 8.1 = 2(3.1 – 1) – 16 8 = 2(2) – 16 8 = 4 – 16 8 = – 12 falso 
7) ( S ) 3(y – 5) + 7y = 5(3 – y), para y = 2 
 3(2–5) + 7.2 = 5(3–2) 3(– 3) + 14 = 5.1 – 9 + 14 = 5 5 = 5 verdade 
8) ( N ) 2a/5 – 2 = a/4 + 4, para a = 1
 2.1: 5 – 2 = 1: 4 + 4 2: 5 – 2 = 1: 4 + 4 (2 – 10) : 5 = (1 + 16) : 4 – 8: 5 = 17 : 4 falso 
III) Resolva as equações de 1o grau.
1) x + 4 = 3 2) 2y + 9 = y = 4
 x = 3 – 4 2y – y = 4 – 9 
 x = – 1 y = – 5 
 
 v = {– 1} v = {– 5}
3) 4z – 8 = 3z – 5 4) 3w + 9 = 2w – 3 
 4z – 3z = – 5 + 8 3w – 2w = – 3 – 9 
 z = + 3 w = – 12 
 v = {+3} v = {– 12} 
5) 9a = 7 6) 4t – 8 = 4
 a = 
 4t = 4 + 8
 4t = 12
 t = 12 : 4
 v = {
} t = 3
 v = {3}
7) 7 + 3x = 11 8) 
r – r = r – 1 
 3x = 11 – 7 
r – 
 = 
 – 
 
 3x = 4 
r – 
 = 
 – 
 x = 
 2r – 3r = 3r – 3 
 – r = 3r – 3 
 v = {
} – r – 3r = – 3
 – 4r = – 3 
 4r = 3
 r = 
 v = {
}
 9) 3(e + 2) – e = e – 1 10) 
 = 
 – 
 3e + 6 – e = e – 1 
 = 
 – 
 3e – e – e = – 1 – 6 x – 2 = 2x – 1 
 3e – 2e = – 7 x – 2x = – 1 + 2
 e = – 7 – x = 1
 x = – 1 
 v = {– 7} v = {– 1}
11) 
 = w 12) 4y – 
 = 3(1 – y)
 
= 
 
 = 
 
 = 
 
 – 
 = 
 2w – 1 = 3w 12y – 2 = 3(3 – 3y) 
 2w – 3w = 1 12y – 2 = 9 – 9y 
 – w = 1 12y + 9y = 9 + 2
 w = – 1 21y = 11
 y = 
 v = {– 1} v = {
}
13) 2(x +3) = 
 – 
 14) y – 2(y + 1) = 
 2x + 6 = 
 – 
 y – 2y + 2 = 
 
 + 
 = 
 – 
 
– 
 + 
 = 
 
 + 
 = 
 – 
 
– 
 + 
 = 
 20x + 60 = 2 – 5 x 2y – 4y + 4 = y
 20x + 5x = 2 – 60 – 2y + 4 = y y = 
 25x = – 58 – 2y – y = – 4 
 x = – 
 – 3y = – 4 
 3y = 4 v = {
}
15) w + 4 = 
 – 2 (w + 1) 16) 
 – 2(x + 1) = 
 
 w + 4 = 
 – 2w – 2 
 – 2x – 2 = 
 
 
 + 
 = 
 – 
– 
 
 – 
– 
= 
 
 + 
 = 
 – 
– 
 
 – 
– 
= 
 5w + 20 = 1 – 10w – 10 3 – 12x – 12 = 2x – 2 
 5w + 10w = 1 – 10 – 20 – 12x – 2x = – 2 – 3 + 12 
 15w = – 29 – 14x = 7
 w = – 
 14x = – 7 
 v = {– 
} x = – 
 
 x = – 
 v = {– 
}
17) – 5(2x – 3) = 
 – 
 18) 3(– 2 – x) – 
 = 4(3x – 1)
 – 10x + 15 = 
 – 
 – 6 – 3x– 
 = 12x – 4 
 – 
 + 
 = 
 – 
 – 
– 
– 
 = 
– 
 – 
 + 
 = 
 – 
 – 
– 
– 
 = 
– 
 – 100x + 150 = 4 – 5x + 5 – 18 – 9x – 1 = 36x – 12 
 – 100x + 5x = 4 + 5 – 150 – 9x – 36x = – 12 + 18 + 1 
 – 95x = – 141 – 45x = 7 
 95x = 141 45x = – 7 
 x = 
 x = – 
 v = {
} v = {– 
}
19) 12 – 3x – 
 = 
 20) 
= 
 – 
 
 
 – 
 – 
 = 
 
= 
 – 
 
 – 
 – 
 = 
 
= 
 – 
 36 – 9x – (x – 1) = x 6.( –4x + 8) = 15 – 10.(x – 1)
 36 – 9x – x + 1 = x – 24x + 48 = 15 – 10x + 10
 – 9x – x – x = – 36 – 1 – 24x + 10x = 15 + 10 – 48
 – 11x = – 37 – 14x = – 23
 11x = 37 14x = 23
 x = 
 x = 
 
 v = {
} v = {
}
 
IV) Resolva as inequações:
1) x – 4 > 6 2) x + 8 > – 2 
 x > 6 + 4 x > – 2 – 8
 x > 10 x > – 10
 v = {x 
 R │x > 10} v = {x 
 R │x > – 10}
3) x + 4 < 8 4) 2x – 4 > x + 1
 x < 8 – 4 2x – x > + 1 + 4
 x < 4 x > 5
 v = {x 
 R │x < 4} v = {x 
 R │x > 5}
5) 10x – 9 < 9x + 1 6) 20x + 1 > 19x + 11
 10x – 9x < + 1 + 9 20x – 19x > + 11 – 1
 x < 10 x > 10
 v = {x 
 R │x < 10} v = {x 
 R │x > 10}
7) 2x + 6 < 6x – 2 8) 3x + 6 < 9x + 1 9) 7x – 1 < – 14x + 6 10) 9x + 6 < 10x + 1
 2x – 6x < – 2 – 6 3x – 9x < + 1 – 6 7x + 14x < + 6 + 1 9x – 10x < + 1 – 6
 – 4x < – 8 – 6x < – 5 21x < 7 – x < – 5
 4x > 8 6x > 5 x < 7 : 7/21 : 7 x > 5
 x > 8 : 4 x > 5/6 x < 1/3
 x > 2
 v = {x 
 R │x > 2} v = {x 
 R │x > 5/6} v = {x 
 R │x < 1/3} v = {x 
 R │x > 5}
11) 19x – 2 > 10x + 5 12) 30x + 21 < 44x + 2
 19x – 10x > + 5 + 2 30x – 44x < + 2 – 21
 9x > 7 – 14x < – 19
 x > 7/9 14x > 19
 x > 19/14
 v = {x 
 R │x > 7/9} v = {x 
 R │x > 19/14}
13) 
+ 2x > 
 14) 2(x + 
) < 3x – 1 
 
 + 
 > 
 2x + 
 < 3x – 1
 
 + 
 > 
 
 + 
 < 
 – 
 2 + 20x > 5 + 5x 
 + 
 < 
 – 
 20x – 5x > 5 – 2 10x + 2 < 15x – 5
 15x > 3 10x – 15x < – 5 – 2 
 x > 
 – 5x < – 7 
 x > 
 5x > 7 x > 
 
 v = {x 
 R │x > 
} v = {x 
 R │x > 
}
15) 4x > 
 – 3(x + 2)
 
> 
 – 
 – 
 20x > 1 – 15x – 30 35x > – 29
 
> 
 – 
 – 
 20x + 15x > 1 – 30 x > – 
 v = {x 
 R │x > – 
}
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