Question

If \[ \left| \frac{2x}{5} \right| = \left| \frac{6 - 5}{4} \right|, \quad \text{then the value of } x \text{ is:} \]

• A. 3
• B. 7
• C. \(\pm 7\)
• D. \(\pm 3\)

Hint:

When solving absolute value equations, remember to consider both the positive and negative cases for the expression inside the absolute value.

Answer 1

The Correct Option is D

First, simplify the right-hand side of the equation: \[ \left| \frac{6 - 5}{4} \right| = \left| \frac{1}{4} \right| = \frac{1}{4}. \] The equation becomes: \[ \left| \frac{2x}{5} \right| = \frac{1}{4}. \] Removing the absolute value yields: \[ \frac{2x}{5} = \pm \frac{1}{4}. \] Solving for \( x \) in each case: 1. If \( \frac{2x}{5} = \frac{1}{4} \), multiplying by 5 gives \( 2x = \frac{5}{4} \), so \( x = \frac{5}{8} \). 2. If \( \frac{2x}{5} = -\frac{1}{4} \), multiplying by 5 gives \( 2x = -\frac{5}{4} \), so \( x = -\frac{5}{8} \). Therefore, \( x = \pm \frac{5}{8} \).