Solving Equations With Variables on Both Sides Lesson Plan

Warm-up 

It will be helpful to start students off with a warm up where they need to combine variable terms on one side before solving the equation. Give students a few minutes to work on the two examples.

You can encourage them to check their answers with a partner when they’re finished. Ask for volunteers if any students want to come to the board and explain how they solved each problem. 

Find the similarities and differences

Show the next slide which asks students to think about what is the same and what is different about the two equations.

Give students a few minutes to think independently, then discuss with a partner. After that, ask for students to explain some of the similarities and differences they found. Some answers you might expect are outlined below:

Similarities:

• Both are equations. 
• Both equations contain the same variables and numbers.
• The equations are equivalent. (This is a tricky one for students to recognize, but some might!)

Differences:

• You can solve the one on the left by combining like terms, then solving.
• On the left, the variable terms are all on one side of the equal sign. On the right, there are variable terms on both sides of the equal sign.

Inverse operations with variable terms

Use this opportunity to talk to students about inverse operations and how we use them to “cancel out” constants. Explain that we can also use inverse operations to cancel out variable terms. Point out the `-7x` in the equation on the right and ask students, “since the `7x` is being subtracted, what can we do to cancel it out?” Students will likely respond that we can add `7x`. Show students how you add `7x` to both sides and simplify to get `4x + 4 = -16`. Combine like terms with the equation on the left to show students that that equation also simplifies to `4x + 4 = -16`! 

Summarize

After that first example, you’ll want to summarize with students the steps to take to solve an equation with variables on both sides. You may want to give students a few minutes to jot this down in their notebooks. Be sure to communicate that if there are no factors to distribute, or no like terms to combine on either side, students can skip right to step `2`!

Canceling the variable term from either side

With this next example, split the class down the middle. Tell the right side of the class to solve the equation by first canceling out the `2x` from the right side. Tell the left side of the class to solve the equation by first canceling out the `5x` from the left side. When students are done solving, choose one students from each side of the classroom to come up to the board and explain how they solved the problem.

This activity is really beneficial for students to see that they can start the problem in different ways and still arrive at the same answer!

More examples as a class

The slideshow contains a few more examples to do as a class. Give students time to try each one on their own, then go over them together. Remind students of the steps to solving equations with variables on both sides.