Question

question
solve the equation for all values of x.
|4x + 8| + 2 = 2x
answer attempt 1 out of 2
additional solution no solution
x =

Explanation:

Step1: Isolate the absolute value

Subtract 2 from both sides.
$|4x + 8| = 2x - 2$

Step2: Set up two cases

Case 1: Inside absolute value is non-negative.
$4x + 8 = 2x - 2$
Case 2: Inside absolute value is negative.
$4x + 8 = -(2x - 2)$

Step3: Solve Case 1

Subtract $2x$, subtract 8.
$4x - 2x = -2 - 8$
$2x = -10$
$x = -5$

Step4: Solve Case 2

Expand right side, collect like terms.
$4x + 8 = -2x + 2$
$4x + 2x = 2 - 8$
$6x = -6$
$x = -1$

Step5: Verify solutions

Check $x=-5$: $|4(-5)+8|+2=|-12|+2=14$, $2(-5)=-10$. $14
eq-10$, invalid.
Check $x=-1$: $|4(-1)+8|+2=|4|+2=6$, $2(-1)=-2$. $6
eq-2$, invalid.

Answer:

No Solution