Question

solve the equation. $\frac{1}{4} - \frac{x}{3} = \frac{25}{12}$

Explanation:

Step1: Find common denominator

The common denominator of 4, 3, 12 is 12. Multiply each term by 12 to eliminate fractions:
$$12 \times \frac{1}{4} - 12 \times \frac{x}{3} = 12 \times \frac{25}{12}$$

Step2: Simplify each term

Calculate each product:
$$3 - 4x = 25$$

Step3: Isolate the variable term

Subtract 3 from both sides:
$$-4x = 25 - 3$$
$$-4x = 22$$

Step4: Solve for x

Divide both sides by -4:
$$x = \frac{22}{-4} = -\frac{11}{2}$$

Answer:

$x = -\frac{11}{2}$