Question:
If
\[
|3x - 2| \leq \frac{1}{2},
\]
then \( x \in \)
If
\[
|3x - 2| \leq \frac{1}{2},
\]
then \( x \in \)
Show Hint
When solving absolute value inequalities, split the inequality into two parts, then solve for the variable.
Updated On: Mar 28, 2026
- \( \left[ \frac{1}{2}, \frac{5}{6} \right] \)
- \( \left( \frac{1}{2}, \frac{5}{6} \right) \)
- \( \left( \frac{1}{2}, \frac{5}{6} \right] \)
- \( \left[ \frac{1}{2}, \frac{5}{6} \right) \)
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The Correct Option is A
Solution and Explanation
Step 1: Solve the inequality.
We are given the inequality: \[ |3x - 2| \leq \frac{1}{2}. \] This implies: \[ -\frac{1}{2} \leq 3x - 2 \leq \frac{1}{2}. \] Now, solve for \( x \) by adding 2 to all parts of the inequality: \[ \frac{3}{2} \leq 3x \leq \frac{5}{2}. \] Next, divide by 3: \[ \frac{1}{2} \leq x \leq \frac{5}{6}. \]
Step 2: Conclusion.
Thus, \( x \) lies in the interval \( \left[ \frac{1}{2}, \frac{5}{6} \right] \), which corresponds to option (A).
We are given the inequality: \[ |3x - 2| \leq \frac{1}{2}. \] This implies: \[ -\frac{1}{2} \leq 3x - 2 \leq \frac{1}{2}. \] Now, solve for \( x \) by adding 2 to all parts of the inequality: \[ \frac{3}{2} \leq 3x \leq \frac{5}{2}. \] Next, divide by 3: \[ \frac{1}{2} \leq x \leq \frac{5}{6}. \]
Step 2: Conclusion.
Thus, \( x \) lies in the interval \( \left[ \frac{1}{2}, \frac{5}{6} \right] \), which corresponds to option (A).
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