Why do students struggle with solving equations that have variables on both sides?

Question

My child understands one-step and two-step equations, but as soon as the variable appears on both sides, they freeze or get confused. Why is this such a common struggle, and how can I help them move forward?

Answer 1

In my experience, students usually struggle with equations that have variables on both sides because they become confused about what to move and what changes when it moves. I teach them to think of the equal sign as a divider. Put all the variables (letters) on one side and all the constants (numbers) on the other.

One of the biggest mistakes students make is forgetting that the sign changes when a term crosses the equal sign.

For example:

+2x becomes -2x

-5 becomes +5

+8 becomes -8

Another common problem is not understanding the difference between a variable and a constant. A variable is simply a letter (such as x), and a constant is simply a number. If there is a positive or negative sign in front of it, the sign is part of the entire term. For example, -4 is one constant, and -2x is one variable term. When you move them to the other side of the equation, move the entire term, not just the number or the letter.

Once students understand these simple rules and practice them consistently, solving equations with variables on both sides becomes much easier and much less intimidating.

Answer 2

I like to tell my students to think of math equations like a balance scale—if you do something to one side, you must do the same to the other to keep things equal. Another helpful tip when solving equations is to remember PEMDAS—but in reverse. When isolating a variable, you typically "undo" operations in the opposite order of operations.

I’ve tutored all the prerequisite college math courses, and this concept comes up again and again. It's a foundational skill that never goes away—and once you master it, solving equations becomes much more intuitive.

Answer 3

I would have to meet with your child to know for certain. But if I have to guess, it's that they don't know how to use proper solving techniques. Some students, especially really bright ones, can easily reason the answer to a one- or two-step problem. And yes, it is a common issue, especially in a standardized test atmosphere of education that is answer driven, and not process driven. But it will create bigger issues as they continue into higher math, so getting them help on that now is crucial.

Answer 4

Many students hit a wall when they first see equations with variables on both sides. It often isn’t because they lack the ability, but because they haven’t yet developed a strong sense of structure and balance in equations.

One of the biggest challenges is understanding that solving an equation is like keeping both sides of a scale balanced. When students move a variable or constant from one side to the other, they need to apply inverse operations carefully and maintain equality throughout. If earlier steps with one-step or two-step equations weren’t fully mastered, that confusion can multiply.

I help students break this down using color coding, algebra tiles, or guided mental models to reinforce structure and logic. We practice identifying like terms, isolating variables step by step, and using checks to build accuracy. Over time, students build confidence and fluency, and solving equations starts to feel less like a guessing game and more like a process they can control.

If your child or student is struggling at this stage, they are not alone. With guided practice, clear modeling, and the right pacing, this topic becomes manageable and often empowering.