Question

Resolva as inequações U = R
a) 8x – 10 > 2x + 8
b) 2(3x +7) < – 4x + 8
c) 20 – (2x +5) ≤ 11 + 8x

Answer 1

Explicação passo a passo:

a)

$\sf{8x - 10 > 2x + 8}$

$\sf{8x - 2x > 8 + 10}$

$\sf{6x > 18}$

$\sf{x > \dfrac{18}{6}}$

$\sf{x > 3}$

$\boxed{\sf{S = \left\{x \mathbf{\in} \mathbb{R} / x > 3\right\}}}$

b)

$\sf{2(3x + 7) < - 4x + 8}$

$\sf{6x + 14 < - 4x + 8}$

$\sf{6x + 4x < 8 - 14}$

$\sf{10x < - 6}$

$\sf{x < - \dfrac{6}{10}}$

$\sf{x < - \dfrac{6\div2}{10\div2}}$

$\sf{x < - \dfrac{3}{5}}$

$\boxed{\sf{S = \left\{x \mathbf{\in} \mathbb{R} / x < - \dfrac{3}{5}\right\}}}$

c)

$\sf{20 - (2x + 5) ≤ 11 + 8x}$

$\sf{20 - 2x - 5 ≤ 11 + 8x}$

$\sf{- 2x - 8x ≤ 11 - 20 + 5}$

$\sf{- 10x ≤ - 4}$

$\sf{10x ≥ 4~~\cdot (-1)}$

$\sf{x ≥ \dfrac{4}{10}}$

$\sf{x ≥ - \dfrac{4\div2}{10\div2}}$

$\sf{x ≥ - \dfrac{2}{5}}$

$\boxed{\sf{S = \left\{x \mathbf{\in} \mathbb{R} / x ≥ - \dfrac{2}{5}\right\}}}$