Skip to content
eurekami
Menu

Free resources

Learn

Exams

Play

For

Sign up freeLog inEspañol

Grades 6 and 7 (Years 6 to 8 in England)

One step equations: how to solve them, with a worksheet

Here is how to solve one step equations by undoing a single operation, with examples for all four operations and a quick way to check every answer. Try the free one step equations practice below, then print a fresh worksheet with an answer key.

The method, step by step

  1. Find the one operation that has been done to the variable.
  2. Choose its inverse: subtract to undo adding, add to undo subtracting, divide to undo multiplying, multiply to undo dividing.
  3. Do that inverse operation to both sides of the equation.
  4. Write the variable on its own with its value, such as x = 9.
  5. Check by putting your answer back into the original equation.

CCSS 6.EE.B.5CCSS 6.EE.B.7England: Y6 AlgebraEngland: KS3 Algebra

Worked example

Solve 7x = 91.

  1. 7x means 7 × x, so x has been multiplied by 7.
  2. The inverse of multiplying by 7 is dividing by 7.
  3. Divide both sides by 7: 7x ÷ 7 = x, and 91 ÷ 7 = 13.
  4. Check: 7 × 13 = 91, which matches the right side.
  5. x = 13.

Practice now

Question 1 of 100 correct

Solve: x − 30 = −15

x − 30=−15

Print a worksheet with answersShare to Google ClassroomFree, no sign-up. Nothing you type is saved.

Print and play

Free printables, made fresh each time you open one. Print as many as you like, or do them on a tablet or computer with a finger, stylus or mouse.

What a one step equation is

An equation says that two amounts are equal. In a one step equation, only one thing has been done to the unknown number, so one step undoes it. x + 8 = 20, y − 5 = 11, 4n = 36 and m ÷ 3 = 9 are all one step equations. The letter is called the variable, and solving the equation means finding the value that makes it true.

Think of a balance scale. x + 8 = 20 means a mystery bag and 8 marbles balance 20 marbles. Take 8 marbles off both pans and it still balances: the bag on its own weighs the same as 12 marbles, so x = 12. Whatever you do to one side, do to the other, and the balance holds.

Inverse operations

Every operation has an opposite, called its inverse, that undoes it. Adding and subtracting undo each other, and so do multiplying and dividing. To solve a one step equation, spot the operation that has been done to the variable, then do its inverse to both sides.

  • Addition: x + 15 = 42. Subtract 15 from both sides, so x = 27.
  • Subtraction: x − 9 = 23. Add 9 to both sides, so x = 32.
  • Multiplication: 6x = 54. Divide both sides by 6, so x = 9.
  • Division: x ÷ 4 = 12, also written x/4 = 12. Multiply both sides by 4, so x = 48.

It doesn't matter which side the variable is on. In 15 = x + 6, the step is the same: subtract 6 from both sides to get 9 = x, which means x = 9.

Decimals, fractions and negative numbers

The method never changes when the numbers get harder. Only the arithmetic does.

  • Decimals: y + 3.6 = 10.2. Subtract 3.6 from both sides, so y = 6.6.
  • Fractions: x + 3/4 = 2 1/2. Subtract 3/4: 2 1/2 − 3/4 = 10/4 − 3/4 = 7/4, so x = 1 3/4.
  • A fraction in front of x: (1/3)x = 7 means a third of x is 7, so multiply both sides by 3 and x = 21.
  • A negative answer: x + 12 = 5 gives x = 5 − 12 = −7.
  • A negative number in front of x: −5x = 40. Divide both sides by −5, so x = −8.

One step equation word problems

In a word problem, pick a letter for the number you don't know, then write the story as an equation. Ask what happens to the unknown: is something added, taken away, multiplied or shared out?

  • Maya had some stickers and was given 18 more. Now she has 45. With s for her starting number, s + 18 = 45, so s = 27.
  • Five concert tickets cost $65 in total. With t for the price of one ticket, 5t = 65, so t = $13.
  • A pizza is cut into equal slices and shared by 4 friends, who get 3 slices each. With p for the number of slices, p ÷ 4 = 3, so p = 12.
  • After spending $14, Leo has $26 left. With m for the money he started with, m − 14 = 26, so m = $40.

Always read the answer back into the story. Five tickets at $13 cost 5 × 13 = $65, so the answer fits.

When an equation needs two steps

Once one step equations feel easy, the next stage is two step equations such as 3x + 4 = 19. There are two operations to undo, in reverse order: subtract 4 to get 3x = 15, then divide by 3 to get x = 5. The two step equations page has more worked examples and its own worksheet.

How it is taught in school

In the US, Common Core teaches in grade 6 that solving an equation means finding the values that make it true, which you can check by substituting (6.EE.B.5). Students write and solve one step equations of the form x + p = q and px = q, where the numbers are whole numbers, fractions or decimals that are not negative (6.EE.B.7). Grade 7 moves on to two step equations of the form px + q = r and p(x + q) = r, including negative numbers (7.EE.B.4.a).

In England, Year 6 pupils express missing number problems algebraically, such as writing n + 7 = 15 for a number that makes 15 when 7 is added. Solving linear equations with algebraic methods is part of Key Stage 3.

How parents can help

  • Start with missing number puzzles such as 8 + ? = 15. A one step equation is the same puzzle with a letter in place of the box.
  • Ask what has been done to x before your child writes anything. Once the operation has a name, the inverse is obvious.
  • Act out the balance with real objects. Coins or buttons in two cupped hands work well.
  • Insist on the check. Putting the answer back into the equation takes seconds and catches most slips.
  • Keep sessions short. Print a fresh worksheet, let your child mark it with the answer key, and read the worked steps together for any they missed.

Common mistakes

  • Doing the same operation instead of its inverse. For x + 7 = 20, adding 7 gives 27, which is wrong; subtracting 7 gives x = 13.
  • Changing one side only. Subtracting 7 on the left but not the right turns x + 7 = 20 into x = 20.
  • Reading 4x as 4 + x. 4x means 4 × x, so in 4x = 28, x is 7, not 24.
  • Dividing the wrong way round. In 6x = 42, x = 42 ÷ 6 = 7, not 6 ÷ 42.
  • Dividing when you should multiply. In x ÷ 5 = 8, x is 5 × 8 = 40. The check shows why: 40 ÷ 5 = 8.
  • Dropping a negative sign. In −3x = 21, x = 21 ÷ (−3) = −7. Check: −3 × (−7) = 21.

Questions people ask

What is a one step equation?
An equation you can solve with a single inverse operation. x + 9 = 20 is one, because subtracting 9 from both sides gives x = 11.
How do you solve one step equations?
Find the operation that has been done to the variable and do the opposite to both sides. For x − 6 = 15, add 6 to both sides, so x = 21.
How do you solve one step equations with multiplication and division?
Divide to undo multiplying, and multiply to undo dividing. 8x = 56 gives x = 7, and x ÷ 3 = 11 gives x = 33.
What is the difference between one step and two step equations?
A one step equation has one operation to undo, like 5x = 30, so x = 6. A two step equation has two, like 5x + 2 = 32: subtract 2, then divide by 5, so x = 6.
How do I check the answer to an equation?
Put your answer in place of the variable and work out both sides. For 9 + y = 25 with y = 16, 9 + 16 = 25, so the answer is right.
What grade learns one step equations?
In the US, grade 6 (6.EE.B.7), with two step equations in grade 7 (7.EE.B.4.a). In England, Year 6 writes missing number problems with letters, and solving equations algebraically is taught in Key Stage 3.
Is there a free one step equations worksheet with answers?
Yes. Use the Print a worksheet button on this page. Each worksheet is freshly made, and the answer key can show answers only or answers with worked steps.

Updated .

Keep exploring

This topic by grade

More math topics

Play it as a game

Math, English and science that click.

Sign up freePricing
One Step Equations Worksheet and Practice | Eurekami