What is the solution of this compound inequality?

Question

asked Jan 20, 2023 193k views

1 Answer

Thivan Mydeen · Answer 1 · 2023-01-25T06:53:53+0000

Answer: -27≥x OR x>7

Explanation:

$\displaystyle\\a)\ -7\geq (x)/(3)+2 \\\\\-7-2\geq (x)/(3)+2-2\\\\ -9\geq (x)/(3) \\\\$

Multiply both parts of the equation by 3:

$\displaystyle\\-9(3)\geq (x)/(3)(3)\\\\\boxed {-27\geq x}$

$\displaystyle\\b)\ (3x+1)/(2) > 11$

Multiply both parts of the equation by 2:

$\displaystyle\\(3x+1)/(2)(2) > 11(2)\\\\3x+1 > 22\\\\3x+1-1 > 22-1\\\\3x > 21$

Divide both parts of the equation by 3:

$\boxed{x > 7}$