Question

hw sec. 2.6
score: 3/8 3/8 answered
question 4
solve for x:
|3x - 3| + 2 = 5
x =
question help: video ebook
submit

Explanation:

Step1: Isolate the absolute value

Subtract 2 from both sides of the equation \(|3x - 3| + 2 = 5\) to get \(|3x - 3| = 5 - 2\).
\( |3x - 3| = 3 \)

Step2: Solve the absolute value equation

The absolute value equation \(|A| = B\) (where \(B\geq0\)) is equivalent to \(A = B\) or \(A = -B\). So we have two cases:

• Case 1: \(3x - 3 = 3\)

Add 3 to both sides: \(3x = 3 + 3\)
\(3x = 6\)
Divide both sides by 3: \(x = \frac{6}{3} = 2\)

• Case 2: \(3x - 3 = -3\)

Add 3 to both sides: \(3x = -3 + 3\)
\(3x = 0\)
Divide both sides by 3: \(x = \frac{0}{3} = 0\)

Answer:

\(x = 0, 2\)