Question

resolva as questões de inequacoes de 1° grau

a) 4×+5> 2×-3
b)5(×+3)-2(×+1)< 2× +3
c)3(× +1)-2>5(×-1)-3(2×-1)

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Answer 1

Resposta:

a)4x+5>2x-3

a)4x+5>2x-3 4x-2x>-3-5

a)4x+5>2x-3 4x-2x>-3-5 2x>-8

a)4x+5>2x-3 4x-2x>-3-5 2x>-8 x>-8/2

a)4x+5>2x-3 4x-2x>-3-5 2x>-8 x>-8/2 x>-4

Answer 2

Resposta:

$a)x > - 4 \\ b)x < - 10 \\ c)x > \frac{7}{4}$

Explicação passo-a-passo:

$\blue{a)4x + 5 > 2x - 3} \\ 4x + 5 > 2x - 3 \\ 4x + 5 - 2x > - 3 \\ 4x - 2 > - 3 - 5 \\ 4x - 2x \\ (4 - 2)x \\ 2x \\ 4x - 2x > - 3 - 5 \\ 2x > - 3 - 5 \\ - 3 - 5 \\ - (3 + 5) \\ - 8 \\ 2x > - 3 - 5 \\ 2x > - 8 \\ 2x \div 2 > - 8 \div 2 \\ x > - 8 \div 2 \\ x > - 4 \\ 2x > - 8 \\ x > - 4 \\ resposta \\ x > - 4 \\ \\ \blue{b)5(x + 3) - 2(x + 1) < 2x + 3} \\ 5(x + 3) - 2(x + 1) < 2x + 3 \\ 5x + 5 \times 3 - 2(x + 1) < 2x + 3 \\5x + 5 \times 3 - 2x - 2 < 2x + 3 \\5 \times 3 \\ 15 \\ 5x + 5 \times 3 - 2x - 2 < 2x + 3 \\ 5x + 15 - 2x - 2 < 2x + 3 \\5x - 2x \\(5 - 2)x \\3x \\5x + 15 - 2x - 2 < 2x + 3 \\ 3x + 15 - 2 < 2x + 3 \\ 3x + 13 < 2x + 3 \\ 3x + 13 - 2x < 3 \\3x - 2x < 3 - 13 \\3x - 2x \\(3 - 2)x \\x \\ 3x - 2x < 3 - 13 \\ x < 3 - 13 \\ x < - 10 \\ resposta \\ x < - 10$

$\blue{c)3(x + 1) - 2 > 5(x + 1) - 3(2x - 1)} \\ 3(x + 1) - 2 > 5(x + 1) - 3(2x - 1) \\ 3x + 3 - 2 > 5(x + 1) - 3(2x - 1) \\3x + 3 - 2 > 5x +5 - 3(2x - 1) \\3x + 3 - 2 > 5x + 5 - 3 \times 2x + 3 \\3 - 2 \\1 \\3x + 3 - 2 > 5x + 5 - 3 \times 2x + 3 \\ 3x + 1 > 5x + 5 - 3 \times 2x + 3 \\ - 3 \times 2 \\ - 6 \\3x + 1 > 5x + 5 - 3 \times 2x + 3 \\3x + 1 > 5 + + 5 - 6x + 3 \\5x - 6x \\(5 - 6)x\\ - 1x \\ - x \\3x + 1 > 5x + 5 - 6x + 3 \\3x + 1 > - x + 5 + 3 \\5 +3 \\ 8 \\ 3x + 1 > - x +5 + 3 \\ 3x + 1 > - x + 8 \\ 3x + 1 + x > 8 \\ 3x + x > 8 - 1 \\ 3x + x \\ (3 + 1)x \\ 4x \\ 3x + x > 8 - 1 \\ 4x > 8 - 1 \\ 4x > 7 \\ 4x \div 4 > 7 \div 4 \\ x > 7 \div 4 \\ \\ x > \frac{7}{4} \\ \\ 4x > 7 \\ \\ x > \frac{7}{4} \\ resposta \\ x > \frac{7}{4}$