Question
Solve for \( x \). \( |6 x-9|=3 \) If there is more than one solution, separate them with commas. If there is no solution, click on "No solution". \( x=\square / \square \)
Ask by Hodgson Vaughan. in the United States
Jan 30,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( x = 1, 2 \)
Solution
To solve the equation \( |6x - 9| = 3 \), we'll consider both scenarios where the expression inside the absolute value can be positive or negative.
1. **First Scenario:**
\[
6x - 9 = 3
\]
\[
6x = 12
\]
\[
x = \frac{12}{6} = 2
\]
2. **Second Scenario:**
\[
6x - 9 = -3
\]
\[
6x = 6
\]
\[
x = \frac{6}{6} = 1
\]
**Solutions:**
\[
x = 1, 2
\]
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Simplify this solution The Deep Dive
To solve the equation \( |6x - 9| = 3 \), we need to consider two cases due to the nature of absolute values. **Case 1:** \( 6x - 9 = 3 \) Add 9 to both sides: \( 6x = 12 \) Now, divide by 6: \( x = 2 \) **Case 2:** \( 6x - 9 = -3 \) Add 9 to both sides: \( 6x = 6 \) Now, divide by 6: \( x = 1 \) Thus, the solutions are \( x = 1, 2 \). So, \( x = 1, 2 \).
