What is the value of x that satisfies the equation \frac{2}{3}x - \frac{1}{4} = \frac{5}{1… — ACT

What is the value of $x$ that satisfies the equation $\frac{2}{3}x - \frac{1}{4} = \frac{5}{12}$ ?

The correct answer is 1. Adding

\frac{1}{4}

to both sides of the equation

\frac{2}{3}x - \frac{1}{4} = \frac{5}{12}

gives

\frac{2}{3}x = \frac{5}{12} + \frac{3}{12} = \frac{8}{12}

. Simplifying

\frac{8}{12}

yields

\frac{2}{3}

, so

\frac{2}{3}x = \frac{2}{3}

. Multiplying both sides by

\frac{3}{2}

isolates

x

, giving

x = 1

Add

\frac{1}{4}

to both sides of the equation to isolate the variable term.

\frac{2}{3}x = \frac{5}{12} + \frac{1}{4}

To solve for

x

, terms containing

x

must be isolated on one side of the equation.

Find a common denominator to add the fractions on the right side.

\frac{2}{3}x = \frac{5}{12} + \frac{3}{12} = \frac{8}{12} = \frac{2}{3}

Fractions must have the same denominator to be added.

Multiply both sides of the equation by the reciprocal of the coefficient of

x

, which is

\frac{3}{2}

x = \frac{2}{3} \cdot \frac{3}{2} = 1

Multiplying a coefficient by its reciprocal yields

1

, isolating the variable

x

Solving single-variable linear equations involving fractions by isolating the variable using inverse operations.

Question