# Let z = x + y/2. Solve for y.

## Question:

Let {eq}z = x + \frac{y}{2} {/eq}. Solve for {eq}y {/eq}.

## Algebraic Expressions

Algebraic expressions are built upon a combination of coefficients that are integers, variables and algebraic operations. Some algebraic operations are addition, subtraction, multiplication and division.

## Answer and Explanation:

To solve for {eq}y {/eq} in the equation below:

{eq}z = x + \frac{y}{2} {/eq}

Isolate the term with {eq}y {/eq} on one side of the equation:

{eq}\displaystyle z - x = \frac{y}{2} {/eq}

Multiplying bothe sides by 2:

{eq}\displaystyle 2(z - x) = \left ( \frac{y}{2} \right) 2 {/eq}

{eq}2(z - x) = y {/eq}

Thus from the equation {eq}z = x + \frac{y}{2} {/eq} the value of {eq}y {/eq} is {eq}y = 2(z - x) {/eq}.

#### Learn more about this topic:

Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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