# Solve the following equation for u: 4u + 8 = -12.

## Question:

Solve the following equation for {eq}u {/eq}: {eq}\; 4u + 8 = -12 {/eq}.

## Simple Algebraic Expressions

An algebraic expression, in the simplest form, is composed of variables, constants or coefficients that are integers and mathematical operators like addition (+), subtraction (-), division ({eq}\displaystyle{ \div }{/eq}) or multiplication ({eq}\displaystyle{ \times }{/eq}).

To solve for {eq}u {/eq} from the equation, the variable should be isolated on one side of the equation:

{eq}4u + 8 = -12 {/eq}

{eq}4u = -12 - 8 {/eq}

{eq}4u = -20 {/eq}

Dividing both sides by {eq}4 {/eq}:

{eq}\displaystyle \frac{4u}{4} = \frac{-20}{4} {/eq}

{eq}\color{blue}{u = -5} {/eq}

To check, substitute the value to the original equation:

{eq}4u + 8 = -12 {/eq}

{eq}4(-5) + 8 \stackrel{?}{=} -12 {/eq}

{eq}-20 + 8 \stackrel{?}{=} -12 {/eq}

{eq}-12 \stackrel{\checkmark}{=} -12 {/eq}

Thus, the value of {eq}u {/eq} in {eq}4u + 8 = -12 {/eq} is {eq}\color{blue}{-5} {/eq}.

Evaluating Simple Algebraic Expressions

from ELM: CSU Math Study Guide

Chapter 6 / Lesson 3
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