Question

Solve the inequality. Enter any fractions as reduced improper fractions. 4x ≤ -2/5(6x + 6) The solution is _____​

Answer 1

Answer:

x≤ -3/8

Step-by-step explanation:

$4x\le \:-\frac{2}{5}\left(6x+6\right)$

Expand ;

$\mathrm{Expand\:}-\frac{2}{5}\left(6x+6\right):\quad -\frac{12}{5}x-\frac{12}{5}$

$4x\le \:-\frac{12}{5}x-\frac{12}{5}\\\\\mathrm{Add\:}\frac{12}{5}x\mathrm{\:to\:both\:sides}\\\\4x+\frac{12}{5}x\le \:-\frac{12}{5}x-\frac{12}{5}+\frac{12}{5}x$

Simplify

$\frac{32}{5}x\le \:-\frac{12}{5}\\\\Multiply \:both\:sides\:by\:5\\5\times\frac{32}{5}x\le \:5\left(-\frac{12}{5}\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\\frac{32x}{32}\le \frac{-12}{32}\\\\Simplify\\x\le \:-\frac{3}{8}$