Question

find the value of x in the equation: 3/4x - 1/3 = 1/2

Explanation:

Step1: Add 1/3 to both sides

To isolate the term with \( x \), we add \( \frac{1}{3} \) to both sides of the equation \( \frac{3}{4}x - \frac{1}{3} = \frac{1}{2} \). This gives us \( \frac{3}{4}x = \frac{1}{2} + \frac{1}{3} \). To add the fractions on the right, we find a common denominator, which is 6. So \( \frac{1}{2} = \frac{3}{6} \) and \( \frac{1}{3} = \frac{2}{6} \), and adding them gives \( \frac{3}{6} + \frac{2}{6} = \frac{5}{6} \). Thus, \( \frac{3}{4}x = \frac{5}{6} \).

Step2: Solve for x

To solve for \( x \), we multiply both sides of the equation \( \frac{3}{4}x = \frac{5}{6} \) by the reciprocal of \( \frac{3}{4} \), which is \( \frac{4}{3} \). So \( x = \frac{5}{6} \times \frac{4}{3} \). Multiplying the numerators gives \( 5 \times 4 = 20 \) and multiplying the denominators gives \( 6 \times 3 = 18 \). So \( x = \frac{20}{18} \), which simplifies to \( \frac{10}{9} \) by dividing both the numerator and denominator by 2.

Answer:

\( \frac{10}{9} \)