If \frac{3}{5}(5x - 10) - \frac{1}{2}(4x - 6) = 12, what is the value of 2x - 5? — SAT

If $\frac{3}{5}(5x - 10) - \frac{1}{2}(4x - 6) = 12$ , what is the value of $2x - 5$ ?

The correct answer is 25.

The correct answer is 25. Distributing the fractions yields

3x - 6 - 2x + 3 = 12

, which simplifies to

x - 3 = 12

, so

x = 15

. Substituting this into

2x - 5

gives

2(15) - 5 = 25

Distribute the coefficients to the terms inside the parentheses.

(3x - 6) - (2x - 3) = 12

To simplify the equation by removing the parentheses.

Combine like terms on the left side of the equation.

x - 3 = 12

To group the variable terms and constant terms together.

Isolate the variable

x

by adding 3 to both sides of the equation.

x = 15

To find the value of

x

Substitute

x = 15

into the expression

2x - 5

2(15) - 5 = 25

To find the final value requested by the question.

Solving linear equations in one variable with grouping symbols and fractions, and evaluating an algebraic expression.

Estimated Time:1m 30s

Question