Start with the meaning
The main questions have whole-number solutions and use positive constants. Understand multiplication notation such as 5x = 5 × x. One contrast, 20 − x = 8, requires care with the unknown being subtracted.
Identify the operation attached to the unknown
For x + 7 = 18, seven is being added to x. Undo addition by subtracting seven from both sides. For 5x = 35, x is multiplied by five, so divide both sides by five.
The inverse operation restores the unknown while preserving equality. Write both sides at each step if you tend to change only one side.
Check in the original equation
If x = 11 is proposed for x + 7 = 18, substitute: 11 + 7 = 18. The statement is true, so the value works.
Checking a rearranged equation can repeat an earlier mistake. Use the original version, and calculate both sides independently.
Notice where the unknown appears
18 = x + 7 has the same solution as x + 7 = 18. Equality works in both directions. You can subtract seven from both sides without moving the unknown first.
But 20 − x = 8 is different from x − 20 = 8. Order matters in subtraction. Think of a missing amount taken from twenty; the amount must be twelve.
Use errors to choose another example
If addition and subtraction items work but multiplication fails, revisit what 5x means. If solutions are mostly right but checks are wrong, practise substitution as a separate step.
After reviewing an error, make a fresh equation with the same structure. Do not simply copy the answer key into the worksheet and treat that as independent success.
Worked examples, step by step
Example 1: Solve x − 9 = 14
- Nine has been subtracted from x. Add nine to both sides.
- x = 14 + 9 = 23.
- Check: 23 − 9 = 14.
Example 2: Solve 6p = 42
- 6p means six times p. Divide both sides by six.
- p = 42 ÷ 6 = 7.
- Check: 6 × 7 = 42.
Example 3: Solve q ÷ 4 = 9
- q has been divided by four. Multiply both sides by four.
- q = 9 × 4 = 36.
- Check: 36 ÷ 4 = 9.
Common mistakes and useful repairs
Subtracting the coefficient
In 5x = 30, five multiplies x; it is not added to it. Divide by five to obtain x = 6.
Applying a remembered rule to the wrong subtraction order
x − 8 = 20 and 20 − x = 8 both have a minus sign, but the unknown plays different roles. Substitute your answer to test it.
Try before revealing
Quick understanding check
Read the check answers
Divide both sides by 7. The coefficient multiplies x, so division undoes it.
15. Multiply both sides by three. Check 15 ÷ 3 = 5.
One-step equations worksheet with worked answers — practice sheet
Work on paper before opening an answer. Print this question sheet with or without a separate worked key; no account is needed.
Name: ____________________ Date: __________
Solve x + 7 = 18.
Show answer and reasoning
x = 11. Subtract seven from both sides. Check 11 + 7 = 18.
Solve y − 8 = 13.
Show answer and reasoning
y = 21. Add eight to both sides. Check 21 − 8 = 13.
Solve 5a = 35.
Show answer and reasoning
a = 7. Divide both sides by five. Check 5 × 7 = 35.
Solve b ÷ 6 = 4.
Show answer and reasoning
b = 24. Multiply both sides by six. Check 24 ÷ 6 = 4.
Solve 17 = c + 9.
Show answer and reasoning
c = 8. Subtract nine from both sides. Check 17 = 8 + 9.
Solve 20 − d = 8.
Show answer and reasoning
d = 12. The amount removed from 20 must be 12. Check 20 − 12 = 8.
A child solves 4m = 28 as m = 24. Explain and repair the error.
Show answer and reasoning
m = 7. They subtracted four instead of dividing by four. Check 4 × 7 = 28.
Write an addition equation with solution t = 6, and check it.
Show answer and reasoning
For example, t + 5 = 11. Substitute six: 6 + 5 = 11. Other equations are valid if their solution is six.
One-step equations worksheet with worked answers — worked answer key
x = 11. Subtract seven from both sides. Check 11 + 7 = 18.
y = 21. Add eight to both sides. Check 21 − 8 = 13.
a = 7. Divide both sides by five. Check 5 × 7 = 35.
b = 24. Multiply both sides by six. Check 24 ÷ 6 = 4.
c = 8. Subtract nine from both sides. Check 17 = 8 + 9.
d = 12. The amount removed from 20 must be 12. Check 20 − 12 = 8.
m = 7. They subtracted four instead of dividing by four. Check 4 × 7 = 28.
For example, t + 5 = 11. Substitute six: 6 + 5 = 11. Other equations are valid if their solution is six.
Choose the next practice step
Use the questions in this guide to practise this specific skill. If you need another explanation, return to One-step equations: keep both sides equal before trying a fresh problem.
Help at home: Ask for the check, not only the answer
Cover the answer key and ask your child to explain one inverse operation. Then ask them to substitute their value into the original. This gives two pieces of evidence about the method.
If they can solve only after seeing the worked example, use a smaller-number question with the same structure and allow a balance drawing. Return to the worksheet when the operation is clearer.
Keep one example of your child’s own working. If the same confusion returns across fresh questions, share that attempt with their teacher and ask which next step fits their current learning.
Questions students and parents ask
Does the worksheet include negative-number solutions?
No. This first set focuses on whole-number solutions. Use the negative-number guide before extending to signed values.
How do I print it?
Use Print practice sheet. The questions print first, followed by a worked answer key on a new page. You can choose Save as PDF in the browser’s print dialogue.
About this resource
BananaLearn created these explanations, diagrams and practice questions. They are not reproduced textbook or past-exam questions. School sequences differ; use the prerequisites to choose a starting point. Read how we prepare learning guides.
Curriculum and teaching references used to check scope:
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