How to Solve Two-Step Equations, Step by Step

An equation is a balance: whatever you do to one side, you must do to the other. A two-step equation needs two moves to get the variable alone. Undo the adding or subtracting first, then the multiplying or dividing.

Try it with your own problem ↓

The steps

Look at what has been done to x. In 3x + 5, x was multiplied by 3, then 5 was added.
Undo the operations in reverse order. First undo the addition or subtraction, by doing the opposite to both sides.
Then undo the multiplication or division, by doing the opposite to both sides.
Check your answer by putting it back into the original equation.

A worked example

Solve 3x + 5 = 20.

x was multiplied by 3 and then 5 was added. Undo the +5 first: subtract 5 from both sides.
3x + 5 − 5 = 20 − 5, which gives 3x = 15.
Now undo the ×3: divide both sides by 3.
3x ÷ 3 = 15 ÷ 3, which gives x = 5.
Check: 3(5) + 5 = 15 + 5 = 20. ✓

x = 5.

Try it with your own problem

Open the free The Balance Scale with this example already filled in. It shows every step, and you can type over it with your own numbers.

Work it out: 3x + 5 = 20Opens The Balance Scale with this example

Or try these

Common mistakes

Doing the multiplication step first. If you divide only 3x by 3, you must divide the 5 and the 20 too. Undo the add or subtract first.
Changing only one side. Whatever you do to the left, do to the right.
Sign errors. To undo +5, subtract 5. To undo −5, add 5.
Skipping the check. Putting the answer back catches nearly every mistake.

Questions people ask

Why do I undo addition before multiplication?

Because the steps happened in the order multiply, then add. To undo them, go backwards, like taking off your shoes before your socks.

What if x is divided, like x/3 + 2 = 7?

Subtract 2 to get x/3 = 5, then multiply both sides by 3 to get x = 15.

What if the variable is on both sides?

Move the x terms to one side first by adding or subtracting, then solve as above. For 5x − 4 = 2x + 8: subtract 2x to get 3x − 4 = 8, add 4 to get 3x = 12, so x = 4.

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