What value of x satisfies the equation \frac{1}{2}(4x - 6) + 3x = \frac{2}{3}(9x - 12)? — Armed Services Vocational Aptitude Battery (ASVAB)

What value of $x$ satisfies the equation $\frac{1}{2}(4x - 6) + 3x = \frac{2}{3}(9x - 12)$ ?

The correct answer is

5

. By distributing the fractions, combining the like terms, and properly using inverse operations to isolate

x

, the equation simplifies step-by-step to

x = 5

Distribute the fractions into the parentheses on both sides of the equation.

2x - 3 + 3x = 6x - 8

Applying the distributive property removes the parentheses and prepares the equation for combining terms.

Combine the like terms on the left side.

5x - 3 = 6x - 8

Simplifying each side individually makes it easier to isolate the variable.

Subtract

5x

from both sides to group the variable terms on the right side.

-3 = x - 8

Keeping the variable coefficient positive reduces the chance of a sign error.

Add

8

to both sides to isolate

x

5 = x

Applying the inverse operation isolates the variable and provides the final solution.

Solving One-Variable Linear Equations

Question