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 )
