Topics
1. Equations & Inequalities in One Variable
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United States of AmericaFL
Grade 912

1.04 Literal equations

Lesson
Practice
Lesson

Concept summary

Some equations involve more than one variable. These are usually still referred to as just equations, but sometimes they are given other names.

Literal equation

An equation that involves two or more variables

Example:

x = 5y+3z

We can use the properties of equality to isolate any variable in a literal equation.

Formula

A type of literal equation that describes a relationship between certain quantities

Example:

A = l\cdot w

where A is area,

l is length, and

w is width.

The same variable might be used to represent different quantities across different formulas. For example, in the formula for the area of a rectangle w is used to represent the width of the rectangle, however in another context w might be used to represent a weight or other value.

Worked examples

Example 1

Solve for x in the following equation:

y = 5 \left(1+x\right)

Approach

We need to rearrange the equation to isolate x. We can use the properties of equality and inverse operations to solve literal equations for a variable, just as we would for linear equations.

Solution

\displaystyle y\displaystyle =\displaystyle 5 \left(1+x\right)
\displaystyle \dfrac{y}{5}\displaystyle =\displaystyle 1+xDivide both sides of the equation by 5
\displaystyle \dfrac{y}{5} -1\displaystyle =\displaystyle xSubtract 1 from both sides of the equation
\displaystyle x\displaystyle =\displaystyle \dfrac{y}{5}-1Symmetric property of equality

Reflection

When rearranging an equation, we reverse the operations acting on the variable we want to isolate in the reverse order of operations. Whatever is done to one side of the equation, must be done to the other to keep the equation balanced.

Example 2

Given the formula for Ohm's law:

V=IR

where V is voltage, I is current and R is resistance.

Write the formula for current.

Approach

The formula for current is Ohm's law with I isolated. We use inverse operations and properties of equality to get the solution.

Solution

\displaystyle V\displaystyle =\displaystyle IR
\displaystyle \dfrac{V}{R}\displaystyle =\displaystyle IDivide both sides of the equation by R
\displaystyle I\displaystyle =\displaystyle \dfrac{V}{R}Symmetric property of equality

Outcomes

MA.912.AR.1.1

Identify and interpret parts of an equation or expression that represent a quantity in terms of a mathematical or real-world context, including viewing one or more of its parts as a single entity.

MA.912.AR.1.2

Rearrange equations or formulas to isolate a quantity of interest.

MA.912.AR.2.1

Given a real-world context, write and solve one-variable multi-step linear equations.

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