How do you solve a linear equation?

Undo what was done to x in reverse order, and do the same thing to both sides each time, until x is alone. Then check by putting your answer back into the original equation.

What does it mean to do the same thing to both sides?

An equation says two things are equal. If you add, subtract, multiply or divide by the same number on both sides, they stay equal, so the solution does not change.

How do you solve an equation with x on both sides?

Collect the x terms on one side first by adding or subtracting x from both sides. Then solve the rest as usual. For 3x + 2 = x + 10, subtract x, subtract 2, then divide by 2 to get x = 4.

How can I check my answer?

Put your answer back into the original equation in place of x. If the left side and the right side are equal, the answer is correct.

Part 10 of 10 · EquationsSee the whole course

How to solve a linear equation, step by step

By The Pip team · October 23, 2026 · 7 min read

Short answer

To solve a linear equation, undo what was done to x, in reverse order, and do the same thing to both sides each time. Keep going until x is alone on one side. Then check your answer by putting it back in.

An equation is a question

The equation 3x − 1 = 11 asks: which number x makes both sides equal? The answer is called the solution. Here it is x = 4, because 3(4) − 1 = 12 − 1 = 11.

Undo in reverse order

Look at what was done to x. In 3x − 1, x was multiplied by 3, and then 1 was subtracted. To get x back, undo those steps in the opposite order: add 1 first, then divide by 3.

3x − 1 = 11
Add 1 to both sides: 3x = 12
Divide both sides by 3: x = 4
Check: 3(4) − 1 = 11 ✓

It is like unwinding a bandage: the last thing wrapped on comes off first.

Do the same thing to both sides

An equation is a balance. If you add 1 on the left, you must add 1 on the right, or the two sides stop being equal. The same goes for subtracting, multiplying and dividing: whatever you do, do it to both sides, and do it to every term.

When x is on both sides

First collect the x’s on one side. Take 3x + 2 = x + 10.

3x + 2 = x + 10
Subtract x from both sides: 2x + 2 = 10
Subtract 2 from both sides: 2x = 8
Divide both sides by 2: x = 4
Check: 3(4) + 2 = 14 and 4 + 10 = 14 ✓

See it as two lines

Each side of an equation is its own function, so each is a line. Here, the left side is y = 3x + 2 and the right side is y = x + 10. The solution is the x where the two lines cross. Try it: press the buttons to do the same thing to both sides.

3x + 2 = x + 10

Each side is a line. They cross at x = 4, and that is the solution.

Watch what happens. Both lines move every time you press a button, but the crossing stays at x = 4. That is why the moves are allowed: doing the same thing to both sides changes the lines, but never the place where they meet. By the end, the left line is y = x and the right is the flat line y = 4, and they cross at x = 4.

Watch it explained in under a minute

The same idea, narrated step by step. Square version for sharing: download the 1:1 video.

The five mistakes to avoid

Changing only one side. Whatever you do to the left, do to the right.
Dividing only one term. In 3x − 1 = 11, dividing by 3 gives x − 1/3 = 11/3, not x − 1 = 11/3. Divide every term, or add 1 first.
Sign slips when moving a term. Subtracting 2 from both sides makes +2 vanish on the left and puts −2 on the right.
Undoing in the wrong order. It works if you are careful, but it is easier to undo addition and subtraction first, then multiplication and division.
Skipping the check. Put your answer back in the original equation. If both sides match, you are done.

Try it yourself

Solve each equation. Tap a question to see the answer.

1. x + 7 = 12

Subtract 7 from both sides: x = 5. Check: 5 + 7 = 12 ✓.

2. 4x − 5 = 11

Add 5: 4x = 16. Divide by 4: x = 4. Check: 4(4) − 5 = 11 ✓.

3. 3x = −x + 6

Add x to both sides: 4x = 6. Divide by 4: x = 1.5. Check: 3(1.5) = 4.5 and −1.5 + 6 = 4.5 ✓.

Where this fits in

This is the first step into equations. You have already used the idea in working backwards from f(x), and the lines you met in this course are exactly what the two sides of an equation draw. For more, see our guide Solve equations visually, or go back to the start of the course.