Question

Resolva as inequaçõesa)2(x+1) + 3x > 5-7x
b)-3x ≤ x+2
c)2/5x - 1/2 ≥ 4x/5 - 1
d)3x/4- 9 < 2x/7 +4

Answer 1

 $a)2(x+1)+3x>5-7x \\ 2x+2+3x>5-7x \\ 5x+2>5-7x \\ 12x>3 \\ x>4$
{x ∈ IR / x > 4}

$b)-3x \leq x+2 \\ -4x \leq 2 \\ x \leq - \frac{1}{2}$
{x ∈ IR / x $\leq -\frac{1}{2}$}

 $c)\frac{2x}{5} - \frac{1}{2} \geq \frac{4x}{5} \\ \\ \frac{4x-5}{10} \geq \frac{4x-5}{10} \\ \\ 4x-5 \geq \frac{40x-50}{5} \\ \\ 4x-5 \geq -5 \\ -4x \geq -5 \\ \\ x \geq \frac{5}{4}$
{x ∈ IR / x ≥ $\frac{5}{4}$}

 $d)\frac{3x}{4} -9< \frac{2x}{7} +4 \\ \\ \frac{3x-36}{4} < \frac{2x+28}{7} \\ \\ 3x-36<8x+112 \\ -5x<148 \\ x < -\frac{148}{5}$
{x ∈ IR / x < $- \frac{148}{5}$}