Question

What is the solution set of this inequality?


`8(x - 5) - 3x \geqslant - 20`




A.

`x \geqslant 4`
B.

`x \geqslant - 3`
C.

`x \leqslant - 12`
D.

`x \leqslant 12`


​

Answer 1

A.

`x\ge \:4`

Explanation:

`8(x-5) -3x\geq -20\\\\\mathrm{Expand\:}8\left(x-5\right)-3x:\quad 5x-40\\\\5x-40\ge \:-20\\\\\mathrm{Add\:}40\mathrm{\:to\:both\:sides}\\\\5x-40+40\ge \:-20+40\\\\Simplify\\\\5x\ge \:20\\\\\mathrm{Divide\:both\:sides\:by\:}5\\\\(5x)/(5)\ge (20)/(5)\\\\Simplify\\\\x\ge \:4`