Class 7 · Maths · 2026-27

Simple equations with Answers

Most Class 7 children can solve x + 7 = 12 without knowing how they did it - they saw the answer. That works until the equation has a variable on both sides, and then there is nothing to see. This sheet builds the method deliberately, starting where guessing still works so the method can be practised before it is needed.

33 questions · 25 minutes · full answer key · free printable PDF · no sign-up

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practice · medium · 25 min

Simple equations

Class 7 Maths · Simple equations · 33 questions with answers

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Most Class 7 children can solve x + 7 = 12 without knowing how they did it - they saw the answer. That works until the equation has a variable on both sides, and then there is nothing to see. This sheet builds the method deliberately, starting where guessing still works so the method can be practised before it is needed.

Solves one-step and two-step equations by doing the same thing to both sides
Handles a variable on both sides without guessing
Expands a bracket correctly before solving
Turns a sentence into an equation and solves it
Checks an answer by substituting it back

Exercise 1 of 3 · 12 questions

Solve. Show the step you did to both sides.

Write the answer · Warm-up

Here’s one done for you

2x + 3 = 11. Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Write the step you did each time, even when the answer is obvious. The whole point of the easy questions is to practise the method while it is not needed, because in three weeks it will be.

1)x + 7 = 12
2)y - 4 = 9
3)3a = 21
4)m ÷ 5 = 6
5)2x + 3 = 11
6)5p - 7 = 18
7)4n + 9 = 1
8)x ÷ 3 + 2 = 5
9)6x + 5 = 41
10)y - 13 = 8
11)7a = 91
12)m ÷ 4 = 9

Answers

1) x = 5. Subtract 7 from both sides.
2) y = 13. Add 4 to both sides.
3) a = 7. Divide both sides by 3.
4) m = 30. Multiply both sides by 5.
5) x = 4. Subtract 3 from both sides to get 2x = 8, then divide by 2.
6) p = 5. Add 7 to both sides to get 5p = 25, then divide by 5.
7) n = -2. Subtract 9 from both sides to get 4n = -8, then divide by 4.
8) x = 9. Subtract 2 to get x ÷ 3 = 3, then multiply both sides by 3.
9) x = 6. Subtract 5 from both sides to get 6x = 36, then divide by 6.
10) y = 21. Add 13 to both sides.
11) a = 13. Divide both sides by 7.
12) m = 36. Multiply both sides by 4.

Exercise 2 of 3 · 11 questions

Solve. The variable is on both sides, or there is a bracket.

Write the answer · Guided

Here’s one done for you

3x + 4 = x + 10. Take x from both sides to leave 2x + 4 = 10, then subtract 4 to get 2x = 6, then divide by 2 to get x = 3. Check by substituting: 3(3) + 4 = 13 and 3 + 10 = 13, so it works. Substituting back takes ten seconds and catches nearly every arithmetic slip - it is the cheapest habit in Class 7 maths.

1)3x + 4 = x + 10
2)5y - 3 = 2y + 9
3)2(x + 3) = 14
4)4(m - 2) = 3m + 1
5)7 - 2x = 1
6)3x - 8 = 13
7)9p + 4 = -14
8)2(x - 5) = 18
9)5y + 2 = 3y + 14
10)4m - 7 = m + 11
11)10 - 3x = 1

Answers

1) x = 3. Subtract x from both sides: 2x + 4 = 10. Subtract 4: 2x = 6. Divide by 2.
2) y = 4. Subtract 2y: 3y - 3 = 9. Add 3: 3y = 12. Divide by 3.
3) x = 4. Divide both sides by 2: x + 3 = 7. Subtract 3. (Expanding to 2x + 6 = 14 works equally well.)
4) m = 9. Expand: 4m - 8 = 3m + 1. Subtract 3m: m - 8 = 1. Add 8.
5) x = 3. Subtract 7: -2x = -6. Divide both sides by -2.
6) x = 7. Add 8 to both sides: 3x = 21. Divide by 3.
7) p = -2. Subtract 4: 9p = -18. Divide by 9.
8) x = 14. Divide both sides by 2: x - 5 = 9. Add 5.
9) y = 6. Subtract 3y: 2y + 2 = 14. Subtract 2: 2y = 12. Divide by 2.
10) m = 6. Subtract m: 3m - 7 = 11. Add 7: 3m = 18. Divide by 3.
11) x = 3. Subtract 10: -3x = -9. Divide both sides by -3.

Exercise 3 of 3 · 10 questions

Form an equation, then solve it.

Write the answer · Practice

Here’s one done for you

'Three times a number added to 5 gives 26.' Let the number be n. Three times it is 3n, adding 5 gives 3n + 5, and that equals 26. Solving gives n = 7. The hardest line is the first one, and it is worth writing 'let n be the number' every single time - naming the unknown is what makes the rest of the sentence translatable.

1)Three times a number, added to 5, gives 26. Find the number.
2)The sum of two consecutive whole numbers is 45. Find them.
3)A father is 4 times as old as his son. Their ages add up to 50. Find both ages.
4)The length of a rectangle is 3 cm more than its breadth, and the perimeter is 26 cm. Find the length and breadth.
5)One-fifth of a number, minus 4, is 6. Find the number.
6)Four times a number, less 7, gives 29. Find the number.
7)The sum of three consecutive whole numbers is 51. Find them.
8)A mother is 3 times as old as her daughter, and their ages add up to 48. Find both ages.
9)The breadth of a rectangle is 4 cm less than its length, and the perimeter is 36 cm. Find both.
10)A number is doubled and 9 is added, giving 25. Find the number.

Answers

1) 3n + 5 = 26, so 3n = 21 and n = 7.
2) n + (n + 1) = 45, so 2n + 1 = 45, 2n = 44 and n = 22. The numbers are 22 and 23.
3) s + 4s = 50, so 5s = 50 and s = 10. The son is 10 and the father is 40.
4) 2(b + b + 3) = 26, so 4b + 6 = 26, 4b = 20 and b = 5. The breadth is 5 cm and the length is 8 cm.
5) n ÷ 5 - 4 = 6, so n ÷ 5 = 10 and n = 50.
6) 4n - 7 = 29, so 4n = 36 and n = 9.
7) n + (n + 1) + (n + 2) = 51, so 3n + 3 = 51, 3n = 48 and n = 16. The numbers are 16, 17 and 18.
8) d + 3d = 48, so 4d = 48 and d = 12. The daughter is 12 and the mother is 36.
9) 2(l + l - 4) = 36, so 4l - 8 = 36, 4l = 44 and l = 11. The length is 11 cm and the breadth is 7 cm.
10) 2n + 9 = 25, so 2n = 16 and n = 8.

While your child works

Ask 'what did you do to both sides?' rather than 'what is the answer?'. A child who cannot say it is guessing, and guessing stops working within a term.
Substituting the answer back is the check. Ten seconds, and it catches nearly every slip.
In word problems, insist on 'let n be...' as the first line. Most of the difficulty is naming the unknown, not the algebra.

Before you print it

What is on this worksheet

3 exercises, 33 questions, about 25 minutes. Every exercise has an answer key, printed on its own page so it can be kept back. 3 exercises start with a question already worked out, so you can check the method before helping.

Exercise	What the child does	Questions	Worked example
1	Written answers	12	Yes
2	Written answers	11	Yes
3	Written answers	10	Yes

The same topic at other levels

Most of these topics are taught over several years rather than in one. If this sheet is too hard or too easy, the same idea at another level is usually the fix.

Quadratic equations— Class 10

More Class 7 Maths worksheets

Each one is a complete sheet with its own answer key, free to print.

Questions parents ask

About this worksheet

My child gets the right answers but cannot explain them. Is that a problem?

In Class 7, yes. Guessing works while the numbers are small and stops working the moment a variable appears on both sides. It is much cheaper to build the method now, while the questions are still easy enough to guess.

Should we use transposition or balancing?

Balancing - doing the same thing to both sides - first, because it explains why transposing works. Transposition is the shortcut, and a child who learns the shortcut first tends to move terms without changing signs.

Does this Class 7 Maths worksheet come with answers?

Yes. Every exercise has a full answer key, and it prints on its own page at the end rather than beside the questions - so you can hand your child the sheet and keep the answers back. Some exercises also show one question already worked out, with the method rather than just the result, which is the part most answer keys leave out.

Is there a free printable PDF?

Yes, and there is no sign-up, no email and no account. The download button at the top of the sheet gives you the whole thing - all 33 questions across 3 exercises, plus the answer key - laid out to print on A4.

How long does this worksheet take?

About 25 minutes for 33 questions, though that is a guide rather than a target. It is designed to be split: the exercises are ordered so stopping halfway still leaves a complete piece of work, which matters more than finishing at this age.

Can I use it if my child is in a different class?

Often, yes - these topics are taught across several years and schools vary in when they arrive. Judge by the questions rather than the class on the label. If the first exercise is a struggle the level below is the better start, and the same topic at other levels is linked further up this page.

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