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

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

Answer: 36

The correct answer is 36.

To solve the equation

\frac{5}{6}(y - 2) - \frac{1}{3}(2y - 5) = \frac{3}{2}

, we first clear the fractions by multiplying the entire equation by the least common denominator, 6, which yields

5(y - 2) - 2(2y - 5) = 9

. Distributing the terms on the left side gives

5y - 10 - 4y + 10 = 9

. Combining like terms simplifies this to

y = 9

. The question asks for the value of

4y

, so we multiply

9

4

to get the final answer of

36

Multiply both sides of the equation by the least common denominator, which is 6.

5(y - 2) - 2(2y - 5) = 9

Multiplying by 6 eliminates the fractions, simplifying the equation.

Distribute the coefficients across the parentheses.

5y - 10 - 4y + 10 = 9

Expanding the terms allows like terms to be combined in the next step.

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

y = 9

Combining

5y - 4y

yields

y

, and combining

-10 + 10

yields

0

, isolating the variable.

Multiply the value of

y

by 4.

4y = 36

The question asks for the value of

4y

rather than just

y

Solving a linear equation in one variable by clearing fractions and combining like terms.

Question