EQ - Solve Equations with Variables on Both Sides Lesson

Solve Equations with Variables on Both Sides

image of globe In this lesson, you will learn to solve equations that have variables on both sides. There are many real world problems that can be solved by this type of equation. To solve this type of equation, you will have to get the terms with variables on one side of the equal sign. Once again, the goal is to isolate the variable on one side of the equation. It is very important in this type of equation that you show each step in the solution to avoid confusion. Are you ready to get started?

Example 1: Remember - group the terms with variables on one side of the equation and simplify.

$LaTeX: 60-3y=9y\\ \textcolor{green}{\:\:\:+3y\:\:\:+3y \:\text{Add 3y to both sides.}}\\ 60=12y\\ \frac{60}{12}=\frac{12y}{12}\:\textcolor{green}{\text{Divide both sides by 12.}}\\ y=5$ $60-3y=9y\\ \textcolor{green}{\:\:\:+3y\:\:\:+3y \:\text{Add 3y to both sides.}}\\ 60=12y\\ \frac{60}{12}=\frac{12y}{12}\:\textcolor{green}{\text{Divide both sides by 12.}}\\ y=5$

Check your solution: 60 - 3(5) = 9(5); 60 - 15 = 45

Example 2: It works with negative numbers too!

$LaTeX: -4y+72=-2y\\ \textcolor{green}{+4y\hspace{1cm}+4y\:\:\text{Add 4y to both sides.}}\\ 72=2y\\ \frac{72}{2}=\frac{2y}{2}\:\:\textcolor{green}{\text{Divide both sides by 2.}}\\ y=36$ $-4y+72=-2y\\ \textcolor{green}{+4y\hspace{1cm}+4y\:\:\text{Add 4y to both sides.}}\\ 72=2y\\ \frac{72}{2}=\frac{2y}{2}\:\:\textcolor{green}{\text{Divide both sides by 2.}}\\ y=36$

Check your solution: -4(36) + 72 = -2(36); -144 + 72 = -72

Investigate

image of stick figure playing tennis Jane enjoys playing tennis and wants to join a Tennis Club. Members at the Daves Creek Tennis Club pay $250 plus $5 per visit to play at the indoor courts. Nonmembers must pay $15 per visit. How many visits must a member make to the courts for it to cost her the same as non-paying members?

Strategy

Summarize the problem, using only key words or phrases and rewrite the problem as a statement.

Jane will pay the same amount as a member or non-member after v trips to the tennis court.

Now, translate this information into an equation with variables on both sides and solve.

$LaTeX: 250+5v=15v\\ \:\:\:\:\textcolor{green}{-5v\:\:\:-5v\:\:\text{Subtract 5v from both sides.}}\\ 250=10v\\ \frac{250}{\textcolor{green}{10}}=\frac{10v}{\textcolor{green}{10} }\textcolor{green}{ \text{Divide both sides by 10.}}\\ v=25$ $250+5v=15v\\ \:\:\:\:\textcolor{green}{-5v\:\:\:-5v\:\:\text{Subtract 5v from both sides.}}\\ 250=10v\\ \frac{250}{\textcolor{green}{10}}=\frac{10v}{\textcolor{green}{10} }\textcolor{green}{ \text{Divide both sides by 10.}}\\ v=25$

Interpret the solution: If Jane joins the Tennis Club, she will have to visit the indoor tennis court 25 times for it to cost the same as a non-member.

Take a look at the video to see more great examples and strategies for solving these types of equations.

This video might be helpful as you combine your skills in solving equations. It gives examples of common mistakes and how to avoid making them. Check it out!

Solve Equations with Variables on Both Sides

Now that you have spent some time learning strategies for solving equations with variables on both sides, you are ready to complete your Equations: Solving Equations with Variables on Both Sides Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key. Links to an external site.

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