Question

Which of the following is the solution to 4|x+2|≥16

Answer 1

`\text{Solve the absolute value}\\\\4|x+2|\geq 16\\\\\text{We can make this equation a lot simpler by dividing both sides by 4}\\\\|x+2|\geq4\\\\\text{According to the absolute value, there can be two outcomes. In this case,}\\\text{it would be either:}\\\\x+2\geq4\,\,or\,\,x+2\leq-4\\\\\text{Solve first outcome:}\\\\x+2\geq4\\\\\text{Subtract both sides by 2}\\\\x\geq2\\\\\text{Solve second outcome:}\\\\x+2\leq-4\\\\\text{Subtract 2 from both sides}\\\\x\leq-6\\\\`

`\boxed{x\geq2\,\,or\,\,x\leq-6}`

Answer 2

x ≥ 2 or x ≤ -6

Explanation:

4|x + 2| ≥ 16

|x + 2| ≥ 4

x + 2 ≥ 4 or -(x + 2) ≥ 4

x ≥ 2 or x + 2 ≤ -4 → x ≤ -6