Question

What is the solution of this compound inequality?

Answer 1

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}`