SumNinja

How to solve one-step equations

About 3 min

Undo the change to the missing number. Make the same change on both sides to keep the equation true.

Imagine a game that adds 17 bonus points to your score. The final score is 54, but the starting score is missing. Call it x. The equation x + 17 = 54 records what happened. To find the start, undo the bonus on both sides.

Find the score before the bonus

Find x in x + 17 = 54.

  1. Undo the added 17

    x+17−17=54−17x+17-17=54-17

    Take 17 from both sides. The left loses the bonus, and both sides still name the same amount.

  2. Read the starting score

    x=37x=37

    The left now has just x. The right is 37. You have found the score before the bonus.

  3. Check it in the first equation

    37+17=5437+17=54

    Put 37 in place of x. Adding the bonus gives 54, so the answer fits the story.

Four ways to undo one change

Adding and subtracting undo each other. Multiplying and dividing do too. For 3x = 15, divide both sides by 3 to get x = 5. Here 3x means 3 × x.

Always change both sides. Removing a number from only one side changes which value makes the equation true. Never divide by zero.

The missing number can be negative. From x + 9 = 5, take 9 from both sides. You get x = −4. Check: −4 + 9 = 5.

Change to xHow to undo it
Add a numberSubtract that number
Subtract a numberAdd that number
Multiply by a nonzero numberDivide by that number
Divide by a nonzero numberMultiply by that number

Try it yourself

Work out an answer and explain your reasoning. Then check the explanation.

Undo subtraction

x−6=9x-6=9

Which change will leave x on its own? Find x, then check your answer.

Show the answerHide the answer
x=15x=15

Add 6 to both sides. Then check that fifteen minus six is nine.

Undo multiplication

5x=355x=35

Find x without guessing. Explain why your step keeps both sides equal.

Show the answerHide the answer
x=7x=7

Divide both sides by 5. Five groups of seven make thirty-five.

Spot the broken equality

x+5=12 ⟶ x=12x+5=12\ \longrightarrow\ x=12

The learner has changed only one side. What is the correct value of x?

Show the answerHide the answer
x=12−5=7x=12-5=7

If you take 5 from the left, you must take 5 from the right too.

Undo more than one operation

For 3x + 4 = 19, undo the added 4 first. This leaves 3x = 15. Then divide by 3 to get x = 5. Work back through the steps in reverse order.

Try 4x + 3 = 31. Subtract 3, then divide by 4: x = 7.

3x+4=19 ⇒ 3x=15 ⇒ x=53x+4=19\ \Rightarrow\ 3x=15\ \Rightarrow\ x=5

Choose the undoing step yourself

Try sums that add or multiply. The game moves x around and changes the values. The extra two-step sums are for paper practice.

2-minute practice · keep going after mistakes · opens in a new tab

Try addition equations Try multiplication equations