If \frac{2}{3}(x - 4) = 6, what is the value of x? — SAT

If $\frac{2}{3}(x - 4) = 6$ , what is the value of $x$ ?

Answer: 13

To solve the linear equation

\frac{2}{3}(x - 4) = 6

, multiply both sides of the equation by

\frac{3}{2}

to isolate

x - 4

. This yields

x - 4 = 9

. Adding

4

to both sides of the equation isolates

x

and gives the value

x = 13

Multiply both sides of the equation

\frac{2}{3}(x - 4) = 6

by the reciprocal of the fraction, which is

\frac{3}{2}

x - 4 = 9

Multiplying a fraction by its reciprocal simplifies it to 1, leaving the term in parentheses isolated on the left side.

Add

4

to both sides of the equation

x - 4 = 9

x = 13

Adding

4

isolates the variable

x

on the left side.

Solving a one-variable linear equation using inverse operations.

Question