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

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

Answer: 11

Evaluating the linear equation by clearing the fractions with a common denominator of 10 gives

6(2x - 4) - 5(x - 3) = 12

. Distributing terms yields

12x - 24 - 5x + 15 = 12

. Combining like terms results in

7x - 9 = 12

. Solving for

x

gives

x = 3

. Finally, substituting

x = 3

into the target expression

5x - 4

yields

5(3) - 4 = 11

Multiply both sides of the equation by 10 to clear the denominators.

6(2x - 4) - 5(x - 3) = 12

The least common denominator of 5 and 2 is 10. Multiplying both sides by 10 simplifies the equation by removing the fractions.

Distribute the constants 6 and -5 into the parentheses.

12x - 24 - 5x + 15 = 12

Applying the distributive property removes the parentheses. Be careful to distribute the negative sign for the second term:

-5 \cdot (x - 3) = -5x + 15

Combine like terms on the left side of the equation.

7x - 9 = 12

Grouping the

x

terms (

12x - 5x = 7x

) and the constant terms (

-24 + 15 = -9

) simplifies the equation.

Isolate the variable term

7x

and solve for

x

x = 3

Adding 9 to both sides gives

7x = 21

. Dividing both sides by 7 yields

x = 3

Substitute the value of

x

into the expression

5x - 4

The question asks for the value of

5x - 4

, not just

x

, so we evaluate

5(3) - 4 = 11

Solving linear equations in one variable by clearing fractions, distributing terms, and isolating the variable.

Question