Question

select all the values of x that make the equation |3x + 4| - 9 = 0 true.
a. $1\frac{2}{3}$

b. $-1\frac{2}{3}$

c. $4\frac{1}{3}$

d. $-4\frac{1}{3}$

e. $5\frac{2}{3}$

f. $-5\frac{2}{3}$

Explanation:

Step1: Isolate the absolute value

Start with the equation \(|3x + 4| - 9 = 0\). Add 9 to both sides to isolate the absolute value expression:
\(|3x + 4| = 9\)

Step2: Set up two cases

The absolute value equation \(|A| = B\) (where \(B \geq 0\)) is equivalent to \(A = B\) or \(A = -B\). So we have two cases:

• Case 1: \(3x + 4 = 9\)
• Case 2: \(3x + 4 = -9\)

Step3: Solve Case 1

For \(3x + 4 = 9\), subtract 4 from both sides:
\(3x = 9 - 4\)
\(3x = 5\)
Divide both sides by 3:
\(x = \frac{5}{3} = 1\frac{2}{3}\) (which is option A)

Step4: Solve Case 2

For \(3x + 4 = -9\), subtract 4 from both sides:
\(3x = -9 - 4\)
\(3x = -13\)
Divide both sides by 3:
\(x = -\frac{13}{3} = -4\frac{1}{3}\) (which is option D)

Answer:

A. \(1\frac{2}{3}\), D. \(-4\frac{1}{3}\)