Teaching Solving Equations with Variables on Both Sides

For many, this is the exact moment where their math trauma and anxiety began—the day a teacher introduced a variable and suddenly "math had letters in it."

To a student who is already struggling with number sense, seeing an x on both sides of an equal sign feels less like a puzzle and more like a foreign language they never wanted to speak. But we can't just skip it; having a solid foundation with equations is the only way to move onto the more complex equations that will get added when solving equations in Algebra II and even Geometry. If the foundation is shaky now, those advanced topics will feel impossible later.

If we don't acknowledge the emotional hurdle of "letters in math" while building that core foundation, no amount of "keep it balanced" metaphors will stick. Here is how I approach Solving Equations with Variables on Both Sides to help students lower their defenses and build genuine algebraic fluency.

My 7-Step Progression to Teaching Equations with Variables on Both Sides

Note: I do not start where many textbooks start, with two step equations. If we want students who struggle with math to be successful we need to back it up and provide the core skills needed for solving equations in Algebra. 

1. Combining Like Terms: Before we solve, we have to simplify. Students need to understand that 3x and 4x are the same "species," but 3x and 4 are not.

2. Distributive Property: We tackle the parentheses hurdle early so it doesn't become a roadblock later.

3. One-Step Equations: Building the core concept of inverse operations (+ vs -, + vs ÷) and balancing equations.

4. Two-Step Equations: This is where most Algebra textbooks start, but my students always needed the prior concept work.

5. Multi-Step Equations: Introducing equations that require simplifying (Steps 1 & 2) before solving.

6. Variables on Both Sides (The Introduction): Transitioning to equations where the "unknown" lives in two places.

7. Variables on Both Sides (Part 2): Tackling the complex versions that include distribution and fractions.

Deep Dive: Solving Equations with Variables on Both Sides (Steps 6 & 7)

By the time my students hit Step 6, they aren't scared of the "letters" anymore because we’ve built the foundation. Here is how I make these final steps stick.

Step 6: Solving Equations with Variables on Both Sides the Introduction

My goal here is to help students see that the variable isn't a scary mystery—it’s just a placeholder for a value that keeps the relationship true.

I love to start by using a balance scale to talk about balancing an equation with variables on both sides. Desmos makes it really easy to visualize what’s happening. I created this short Desmos activity to do as a whole class (no students on devices, just the teacher logged in and demoing in front of the class) and you’re welcome to use it with your students too. 

First: I tell students that if we want to find out how much x weighs, we need a single x on one side of the scale and the weight on the other. Then we talk about what I would take off of each side in order to get to that goal.

Next: I help them move from the concrete to the abstract. I write the equation that is being shown on the Desmos scale on the board and as we talk about what to move I show what is happening mathematically to the equation with each step we take.

Step 7: Solving Equations with Variables on Both Sides Part 2

Once these types of equations are making more sense,  I like to move onto a Scavenger Hunt like this Solving Equations With Variables On Both Sides | Printable Scavenger Hunt. Scavenger Hunts are the perfect next step for students who struggle with solving equations in Algebra because they are self checking, they are kinesthetic and get students up and moving around the room (or hallway and require students to focus on only one problem at a time.

Want to build students’ confidence in mathematics? 

Reserve your spot for my free Math Intervention Masterclass: 3 Secrets to Teaching Algebra to Students Who Can’t Multiply and leave with explicit instructional strategies, how to handle foundational skill gaps and proven engagement activities.