Question

question
solve for all values of ( x ) in simplest form.
( |-2x + 11| = 31 )
answer
( oplus ) additional solution ( ominus ) no solution
( x = square )

Explanation:

Step1: Split absolute value into two cases

For $|A|=B$, solve $A=B$ and $A=-B$:
Case 1: $-2x + 11 = 31$
Case 2: $-2x + 11 = -31$

Step2: Solve Case 1 for $x$

Subtract 11 from both sides:
$-2x = 31 - 11$
$-2x = 20$
Divide by -2:
$x = \frac{20}{-2} = -10$

Step3: Solve Case 2 for $x$

Subtract 11 from both sides:
$-2x = -31 - 11$
$-2x = -42$
Divide by -2:
$x = \frac{-42}{-2} = 21$

Answer:

$x = -10$ and $x = 21$