1 Answer

Zelix · Answer 1 · 2022-05-17T07:41:48+0000

Recall the definition of absolute value:

$|x| = \begin{cases} x & \text{if } x \ge 0 \\ -x & \text{if } x < 0 \end{cases}$

Then we have a few cases to consider:

• If
$4x-5\ge0$ and
$-x+5\ge0$ , the equation simplifies to

$4x-5 = -x+5 \implies 5x=10 \implies \boxed{x=2}$

• If
4x-5<0 and
$-x+5\ge0$ , we get

$-(4x-5) = -x + 5 \implies -3x = 0 \implies \boxed{x=0}$

• If
$4x-5\ge0$ and
-x+5<0 , then

$4x-5 = -(-x+5) \implies 3x=0 \implies x=0$

but we already have this solution.

• If
4x-5<0 and
-x+5<0 , then

$-(4x-5) = -(-x+5) \implies -5x = -10 \implies x=2$

which we also already found.

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