Question

solve for x.
4|3x - 6| - 5 = 7
use a comma to separate solutions, as needed. enter each solution as an integer or reduced fraction.
decimal answers will not be accepted. if there is no solution, type dne in the answer box.
x =
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Explanation:

Step1: Isolate absolute value term

Add 5 to both sides:
$4|3x - 6| = 7 + 5$
$4|3x - 6| = 12$

Step2: Simplify absolute value equation

Divide both sides by 4:
$|3x - 6| = \frac{12}{4}$
$|3x - 6| = 3$

Step3: Split into two linear equations

Apply absolute value rule $|A|=B \Rightarrow A=B$ or $A=-B$:
$3x - 6 = 3$ or $3x - 6 = -3$

Step4: Solve first linear equation

Add 6, then divide by 3:
$3x = 3 + 6$
$3x = 9$
$x = \frac{9}{3} = 3$

Step5: Solve second linear equation

Add 6, then divide by 3:
$3x = -3 + 6$
$3x = 3$
$x = \frac{3}{3} = 1$

Answer:

$1, 3$