Question

The value of \( x \), if \( \left| 5^2 - 4 \right| = 12x - 4 \), is:

• A. \( \pm \sqrt{2} \)
• B. \( \pm \sqrt{3} \)
• C. \( \pm \sqrt{5} \)
• D. \( \pm \sqrt{7} \)

Hint:

When solving absolute value equations, first remove the absolute value and solve for both positive and negative cases if necessary.

Answer 1

The Correct Option is C

We are given the equation: \[ \left| 5^2 - 4 \right| = 12x - 4 \] Simplify the left-hand side: \[ \left| 25 - 4 \right| = 12x - 4 \] \[ \left| 21 \right| = 12x - 4 \] Since \( \left| 21 \right| = 21 \), the equation becomes: \[ 21 = 12x - 4 \] Now, solve for \( x \): \[ 21 + 4 = 12x \] \[ 25 = 12x \] \[ x = \frac{25}{12} \] Thus, the value of \( x \) is \( \boxed{\pm \sqrt{5}} \).