Solve the following equations with absolute value.
(B) $5\mid 6x-9\mid +3=3$

• A. $x=-\frac{3}{2}$
• B. $x=0$
• C. $x=\frac{3}{2}$
• D. $x=3$

Answer: (C)

Verified step by step guidance

1. Start with the given equation: \(5\left|6x - 9\right| + 3 = 3\).
2. Isolate the absolute value expression by subtracting 3 from both sides: \(5\left|6x - 9\right| = 3 - 3\).
3. Simplify the right side: \(5\left|6x - 9\right| = 0\).
4. Divide both sides by 5 to solve for the absolute value: \(\left|6x - 9\right| = 0\).
5. Recall that the absolute value of an expression equals zero only when the expression inside is zero, so set \$6x - 9 = 0\( and solve for \)x$.