If 3(2y - 5) - 4(y - 2) = 11, what is the value of 3y + 2? — SAT

If $3(2y - 5) - 4(y - 2) = 11$ , what is the value of $3y + 2$ ?

The correct value is obtained by first distributing the terms, simplifying the equation to find the value of

y

, and then evaluating the expression

3y + 2

. Specifically, distributing yields

6y - 15 - 4y + 8 = 11

, which simplifies to

2y - 7 = 11

. Adding

7

to both sides gives

2y = 18

, so

y = 9

. Substituting

y = 9

into

3y + 2

gives

3(9) + 2 = 29

Distribute the coefficients outside the parentheses.

6y - 15 - 4y + 8 = 11

To simplify the linear equation, we must first remove the parentheses by multiplying the terms inside by the factors outside.

Combine like terms on the left side of the equation.

2y - 7 = 11

Combining the variable terms (

6y - 4y = 2y

) and constant terms (

-15 + 8 = -7

) simplifies the equation.

Isolate the variable term by adding 7 to both sides, then divide by 2.

y = 9

Adding 7 gives

2y = 18

, and dividing by 2 isolates

y

Substitute the value of

y

into the expression

3y + 2

3(9) + 2 = 29

The question asks for the value of the expression

3y + 2

, not just the variable

y

Linear Equations in One Variable

Question