Question

Solve the absolute value equation for x.

|4 - 2x| + 6 = 18

Enter your answers in the blanks in order from least to greatest.

x = first answer or second answer.
(they are both numbers)

Answer 1

Answer:

x = 8 or -4

Step-by-step explanation:

For Simple Absolute Equation:

$\boxed{|x|=\pm x=x\ or\ -x}$

First we group the absolute on 1 side and all constants on the other side:

$|4-2x|+6=18$

$|4-2x|=18-6$

$|4-2x|=12$

Since $|x|=\pm x$, then $|4-2x|=\pm(4-2x)$

$\pm(4-2x)=12$

(i) for |4 - 2x| = 4 - 2x:

   $4-2x=12$

   $4-12=2x$

   $x=-8\div2$

   $x=-4$

(ii) for |4 - 2x| = -(4 - 2x):

    $-(4-2x)=12$

    $-4+2x=12$

    $2x=12+4$

    $x=16\div2$

    $x=8$

Therefore, $\bf x=8\ or\ -4$

*Note: this method is only applicable for 1 absolute value (single absolute value). For equation that has more than 1 absolute value, we have to use multiple absolute value method.