If \frac{2}{3}(6x - 9) - \frac{3}{4}(4x - 8) = \frac{1}{2}(x + 10), what is the value of x… — SAT

If $\frac{2}{3}(6x - 9) - \frac{3}{4}(4x - 8) = \frac{1}{2}(x + 10)$ , what is the value of $x$ ?

Answer: 10

The correct answer is 10.

Distributing the fractions on the left-hand side of the equation simplifies the expression to

x

. Setting this equal to the right-hand side yields the equation

x = \frac{1}{2}(x + 10)

. Multiplying both sides by 2 gives

2x = x + 10

, and subtracting

x

from both sides gives the correct value of 10.

Distribute the fraction

\frac{2}{3}

to the terms inside the first parentheses,

(6x - 9)

, and distribute the fraction

-\frac{3}{4}

to the terms inside the second parentheses,

(4x - 8)

4x - 6 - 3x + 6 = \frac{1}{2}(x + 10)

Applying the distributive property removes the parentheses so that like terms can be combined.

Combine the variable terms and constant terms on the left side of the equation.

x = \frac{1}{2}(x + 10)

Combining

4x

and

-3x

yields

x

, while

-6

and

6

cancel each other out.

Multiply both sides of the equation by 2 to eliminate the fraction.

2x = x + 10

Multiplying by the denominator simplifies the equation by removing the fraction.

Subtract

x

from both sides of the equation to isolate the variable.

x = 10

Subtracting

x

isolates the variable

x

on the left side of the equation.

Solving linear equations in one variable by applying the distributive property and combining like terms.

Question