+26396 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 )
+130462 l -4x l = 32
We have that either
-4x = 32 or -4x = -32
So.......obviously.....x can equal either -8 or 8
+26396 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 )
