Question

solve for all values of x in simplest form.
21 = |-2x + 5|
answer
additional solution no solution
x =

Explanation:

Step1: Split absolute value into two cases

For $|A|=B$, $A=B$ or $A=-B$. So:
$-2x + 5 = 21$ or $-2x + 5 = -21$

Step2: Solve first equation

Subtract 5 from both sides:
$-2x = 21 - 5$
$-2x = 16$
Divide by -2:
$x = \frac{16}{-2} = -8$

Step3: Solve second equation

Subtract 5 from both sides:
$-2x = -21 - 5$
$-2x = -26$
Divide by -2:
$x = \frac{-26}{-2} = 13$

Answer:

$x = -8$ or $x = 13$