brizgney58z

2023-02-27

How to graph and solve $|2x+4|<8$?

Rory Hess

(1)$2x+4\ge 0\to x\ge -2$ the absolute bars have no effect:
$2x+4<8\to x<2$
These two logically imply that $-2\le x<2$
(2)$2x+4\le 0\to x\le -2$ the absolute bars flip the signs
$-2x-4<8\to$ now add $2x+4$ on both sides:
$0<8+2x+4\to$ now subtract $12$:
$-12<2x\to -6-6$
So $-6
By combining the two numbers, the result is:
$-6
graph{|2x+4| [-13.53, 11.78, -2.08, 10.58]}

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