|-4x|=32

Solve each equation. Check your answer. |-4x|=32 

 $$\small{
\begin{array}{rcll}
|-4x| & = & 32 &\qquad \text{(square both sides)}\\
( |-4x| )^2 & = & 32^2 \\
(-4)^2\cdot x^2 &=& 32^2 & \qquad \text{(remove brackets)}\\
4^2 \cdot x^2 &=& 32^2 \\
4^2 \cdot x^2 - 32^2 &=& 0\\
(4x-32)\cdot(4x+32) &=& 0\\
\end{array}$$

(1) 4x-32 = 0  -> 4x = 32 ->  x = 32/4 -> x = 8

(2) 4x+32= 0  -> 4x=-32 ->  x = -32/4 -> x = -8

(1) | -4 * 8 | = |-32| = 32 ( okay )

(2) | -4*(-8) | = | 32 | = 32 ( okay )

l -4x l  =  32

We have that either

-4x = 32        or     -4x = -32

So.......obviously.....x can equal either -8  or 8