Question

What is the solution to the inequality? -2/3(2x - 1/2) ≤ 1/5x - 1 Express your answer in interval notation.

Answer 1

ANSWER

$-\frac{2}{3}(2x-\frac{1}{2})\le \frac{1}{5}x-1$

Multiply through by LCM of 15

$(15) \times -\frac{2}{3}(2x-\frac{1}{2})\le 15(\frac{1}{5}x-1)$

$-10(2x-\frac{1}{2})\le 3x-15$

Expand brackets to obtain,

$-20x+5\le 3x-15$

Group like terms

$15+5\le 20x+3x$

$20\le 23x$

$\frac{20}{23}\le x$

$x\ge \frac{20}{23}$

In interval form it is written as

$[\frac{20}{23}, \infty)$