Determine the value of the variable y that satisfies the given linear equation. — Armed Services Vocational Aptitude Battery (ASVAB)

Determine the value of the variable $y$ that satisfies the given linear equation.

Answer:Given the equation

5(y - 2) + 3y = 4y + 26

, the value of

y

is 【9】.

By distributing the

5

to obtain

5y - 10

, combining the

y

terms on the left to get

8y

, and subsequently isolating

y

through basic inverse operations (

8y - 4y = 26 + 10

), we determine that

4y = 36

, making

y = 9

Distribute the 5 to the terms inside the parentheses.

5y - 10 + 3y = 4y + 26

Applying the distributive property removes the parentheses, allowing like terms to be combined.

Combine the like terms on the left side of the equation.

8y - 10 = 4y + 26

Simplifying each side individually makes it easier to isolate the variable.

Subtract

4y

from both sides of the equation.

4y - 10 = 26

This groups all terms containing the variable

y

on one side of the equation.

Add 10 to both sides of the equation.

4y = 36

This isolates the variable term by removing the constant from the left side.

Divide both sides by 4.

y = 9

Dividing by the coefficient of

y

yields the final value.

Solving linear equations with variables on both sides using the distributive property

Question