Question

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

Answer 1

x≤ -3/8

Explanation:

`4x\le \:-(2)/(5)\left(6x+6\right)\\`

Expand ;

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

`4x\le \:-(12)/(5)x-(12)/(5)\\\\\mathrm{Add\:}(12)/(5)x\mathrm{\:to\:both\:sides}\\\\4x+(12)/(5)x\le \:-(12)/(5)x-(12)/(5)+(12)/(5)x`

Simplify

`(32)/(5)x\le \:-(12)/(5)\\\\Multiply \:both\:sides\:by\:5\\5*(32)/(5)x\le \:5\left(-(12)/(5)\right)\\\\Simplify\\32x\le \:-12\\\\Divide \:both\:sides\:by\:32\\(32x)/(32)\le (-12)/(32)\\\\Simplify\\x\le \:-(3)/(8)`