If \frac{5}{3}(3x - 6) - \frac{1}{2}(4x + 8) = 2, what is the value of 3x - 5? — SAT

If $\frac{5}{3}(3x - 6) - \frac{1}{2}(4x + 8) = 2$ , what is the value of $3x - 5$ ?

Answer: 11

Distributing the fraction

\frac{5}{3}

(3x - 6)

yields

5x - 10

. Distributing the term

-\frac{1}{2}

(4x + 8)

yields

-2x - 4

. Combining these results gives

(5x - 2x) + (-10 - 4) = 2

, which simplifies to

3x - 14 = 2

. Adding 14 to both sides yields

3x = 16

. Finally, subtracting 5 from both sides of this equation gives

3x - 5 = 11

Distribute

\frac{5}{3}

and

-\frac{1}{2}

to the terms within their respective parentheses.

5x - 10 - 2x - 4 = 2

This removes the parentheses and allows us to group terms.

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

3x - 14 = 2

Simplifying the expression on the left side makes it easier to solve.

Add 14 to both sides of the equation to isolate the term

3x

3x = 16

Since the question asks for the value of

3x - 5

, isolating

3x

allows direct evaluation.

Subtract 5 from both sides of the equation

3x = 16

3x - 5 = 11

This directly yields the required value without needing to compute the fractional value of

x

first.

Solving linear equations in one variable by distribution, combining like terms, and evaluating expressions.

Estimated Time:1m 30s

Question