Question

1-Variable Equations & Inequalities Unit Test
2 of 162 of 16 Items



Question
Solve the absolute value equation 6−2|3x+2|−9=−11
.(1 point)
Responses

x=−5
and x=113
x equals negative 5 and x equals Start Fraction 11 over 3 End Fraction

x=23
x equals Start Fraction 2 over 3 End Fraction

no solution
no solution

x=−2
and x=23

Answer 1

To solve the absolute value equation \( 6 - 2|3x + 2| - 9 = -11 \), let's simplify it step by step.

1. First, combine the constants on the left side:
\[
6 - 9 = -3
\]
So, the equation simplifies to:
\[
-3 - 2|3x + 2| = -11
\]

2. Next, isolate the absolute value term:
\[
-2|3x + 2| = -11 + 3
\]
\[
-2|3x + 2| = -8
\]

3. Divide both sides by -2:
\[
|3x + 2| = 4
\]

4. Now, we will set up two equations to solve for \( x \):
- Case 1: \( 3x + 2 = 4 \)
- Case 2: \( 3x + 2 = -4 \)

### Solving Case 1:
\[
3x + 2 = 4
\]
Subtract 2 from both sides:
\[
3x = 2
\]
Now divide by 3:
\[
x = \frac{2}{3}
\]

### Solving Case 2:
\[
3x + 2 = -4
\]
Subtract 2 from both sides:
\[
3x = -6
\]
Now divide by 3:
\[
x = -2
\]

### Final Solutions:
Thus, the solutions to the equation \( 6 - 2|3x + 2| - 9 = -11 \) are
\[
x = -2 \quad \text{and} \quad x = \frac{2}{3}
\]

Based on the provided responses, the correct answer is:
- \( x = -2 \) and \( x = \frac{2}{3} \)