How to Solve Algebra Equations Step by Step

Algebra is the topic that makes many students nervous. Letters instead of numbers? Solving for x? It can feel like a completely different subject from the arithmetic you are used to. But here is the thing: solving an equation is really just finding a missing number. If you can think of it that way, the anxiety drops and the logic takes over.

What is an equation?

An equation is a statement that two things are equal. The equals sign is the key. Whatever is on the left side has the same value as whatever is on the right side.

When we write x + 5 = 12, we are saying "some number plus 5 equals 12." Solving the equation means finding what that number is.

The balance method

Think of an equation as a balance scale. Both sides weigh the same. To keep the scale balanced, anything you do to one side you must also do to the other. This single idea is the foundation of solving every equation.

If you add 3 to the left side, add 3 to the right. If you divide the left side by 2, divide the right side by 2. As long as you do the same operation to both sides, the equation stays true.

One-step equations

These are the simplest type. The variable has one operation applied to it, and you need to undo that operation.

Example 1: x + 7 = 15

The 7 is being added to x. To undo addition, subtract 7 from both sides.

x + 7 - 7 = 15 - 7
x = 8

Example 2: x - 3 = 10

The 3 is being subtracted. To undo subtraction, add 3 to both sides.

x - 3 + 3 = 10 + 3
x = 13

Example 3: 4x = 20

The x is being multiplied by 4. To undo multiplication, divide both sides by 4.

4x / 4 = 20 / 4
x = 5

Example 4: x / 3 = 6

The x is being divided by 3. To undo division, multiply both sides by 3.

(x / 3) x 3 = 6 x 3
x = 18

Two-step equations

These have two operations to undo. The general approach is to undo addition or subtraction first, then undo multiplication or division. Think of it as peeling off layers, starting with the outermost one.

Example 1: 2x + 3 = 11

Undo the addition. Subtract 3 from both sides: 2x = 8.
Undo the multiplication. Divide both sides by 2: x = 4.

Check: 2(4) + 3 = 8 + 3 = 11. Correct.

Example 2: 5x - 7 = 18

Add 7 to both sides: 5x = 25.
Divide both sides by 5: x = 5.

Check: 5(5) - 7 = 25 - 7 = 18. Correct.

Example 3: x/4 + 2 = 9

Subtract 2 from both sides: x/4 = 7.
Multiply both sides by 4: x = 28.

Check: 28/4 + 2 = 7 + 2 = 9. Correct.

Equations with the variable on both sides

Once you are comfortable with two-step equations, you will encounter equations where x appears on both sides. The strategy is to collect all the x terms on one side first.

Example: 3x + 4 = x + 12

Subtract x from both sides to get all x terms on the left: 2x + 4 = 12.
Subtract 4 from both sides: 2x = 8.
Divide both sides by 2: x = 4.

Check: Left side: 3(4) + 4 = 16. Right side: 4 + 12 = 16. Both sides equal 16. Correct.

Equations with brackets

If the equation has brackets, expand them first using the distributive law, then solve as normal.

Example: 3(x + 2) = 21

Expand: 3x + 6 = 21.
Subtract 6: 3x = 15.
Divide by 3: x = 5.

Alternative method: You could also divide both sides by 3 first to get x + 2 = 7, then subtract 2 to get x = 5. Both approaches work. Choose whichever feels more natural.

Always check your answer

Substituting your answer back into the original equation takes 10 seconds and catches mistakes. Get into the habit now. In exams, it is the easiest way to pick up marks you might otherwise lose.

Common mistakes

Doing an operation to only one side. Whatever you do to the left, you must do to the right. No exceptions.
Sign errors. When you subtract a negative or move a negative term, double-check the sign. This is the number one source of algebra errors at every level.
Rushing through steps. Write each step on a new line. It is not slower in practice, because you make fewer mistakes and spend less time going back to fix them.
Forgetting to expand brackets. If you see brackets, deal with them before trying to isolate x.

Building confidence

Algebra is a skill, not a talent. The students who are good at it are the ones who have done lots of practice and are comfortable with the balance method. Start with one-step equations until they feel automatic, then move to two-step, then variables on both sides. Do not skip ahead until each level feels solid.

imSteyn covers algebra equations from the basics in Year 7 through to more complex problems in Years 8 and 9, following the Australian Curriculum. It uses a Socratic approach, guiding you through each step with questions rather than just showing the solution, which helps the method stick. Sign up for free to try it out.

Once you are comfortable solving basic equations, you have a foundation that carries through to every branch of maths that follows: graphing, quadratics, simultaneous equations, and beyond. It is one of the most valuable skills you can build.