Grade 7 · Math · Unit 8 of 12
Two-Step Equations
Undo, undo, solve for x
What your child practises
Solving equations like 3x + 5 = 26 by undoing each step on both sides, writing equations from word problems and checking solutions.
NWT Curriculum learning standard: Two-step equations with whole-number coefficients, constants and solutions
How we explain it
Children can open this short lesson before they practise.
- Keep the equation balanced: do the same to both sides.
- Undo the adding or subtracting first.
- Then undo the multiplying or dividing.
Example: 2x + 3 = 11 Subtract 3 from both sides: 2x = 8. Divide both sides by 2: x = 4. Answer: x = 4
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
On a balance scale, 2 identical bags of marbles plus 15 loose marbles balance 23 loose marbles. How many marbles are in each bag?
⚖️2x + 15 = 23answer box
4
Hint: Take 15 marbles off both sides: 2 bags balance 8 marbles. Share them among 2 bags: 8 ÷ 2 = 4.
Question 2
Which equation matches this sentence? "Two times a number, minus 3, equals 9."
- 2(n − 3) = 9
- 2n + 3 = 9
- 2n − 3 = 9
- 3n − 2 = 9
2n − 3 = 9
Hint: "Two times a number" is 2n. "Minus 3" subtracts 3 after multiplying: 2n − 3. "Equals 9" finishes it: 2n − 3 = 9.
Question 3
Solve for x.
55 = 7x − 8
answer box
9
Hint: The x can be on either side. Add 8 on both sides: 63 = 7x. Then divide by 7: x = 9.
Question 4
A rectangle has a perimeter of 114 cm and a width of 18 cm. What is its length?
answer boxcm
39 cm
Hint: Perimeter = 2L + 2w, so 2L + 36 = 114. Subtract 36: 2L = 78. Divide by 2: L = 39 cm.
Question 5
Solve for x.
5x + 11 = 86
answer box
15
Hint: Undo the + 11 first: subtract 11 from both sides to get 5x = 75. Then undo the × 5: divide both sides by 5 to get x = 15.
Question 6
Is x = 3 a solution of 6x − 11 = 1?
6x − 11 = 1
- Yes
- No
No
Hint: Substitute x = 3: 6 × 3 − 11 = 7. That isn't 1, so x = 3 is not a solution.