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Multi-Step Equations Practice

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Multi-Step Equations Practice

Solve each equation by keeping both sides balanced. Show your working, then check your answer by substituting it into the original equation. Use NZ dollars in the final problem.

Mission 1: Unlock the equations

Find the value of each unknown. Undo addition or subtraction first, then multiplication or division as needed.

1.A robot’s code is hidden in 3x + 5 = 26. What is x? Show the inverse operations you use.

2.Solve 4y − 9 = 27. Which value of y makes the equation true?

3.A number is doubled, then 11 is added. The result is 35. Write an equation and solve to find the number.

Mission 2: Brackets and balance

Brackets show which operation is grouped. Expand carefully or undo the operations in reverse order.

4.Solve 5(a + 2) = 40. Show how you remove the brackets or undo the multiplication.

5.Solve 3(2m − 1) = 21. Give the value of m and check it in the original equation.

6.A student solves 2(x + 4) = 18 by writing 2x + 4 = 18. Is this correct? Explain the mistake and solve the equation.

Mission 3: Choose a route

Some equations have the unknown on both sides. Gather the unknown terms on one side and constants on the other.

7.Solve 7p − 4 = 3p + 20. Show the steps you use to collect the p terms.

8.Which equation has the solution t = 5? Select one, then verify it by substitution.

3t + 2 = 17
4t − 1 = 16
2(t + 3) = 18
5t + 4 = 25

9.True or false: If you subtract 6 from the left side of an equation, you must also subtract 6 from the right side to keep the equation balanced. Explain briefly.

Mission 4: The market-stall challenge

A stall packs the same number of apples into each bag. Use an equation to solve the problem and explain what your answer means.

10.Three identical bags of apples and a 2 kg box together weigh 17 kg. Let w be the mass in kilograms of one bag. Write and solve an equation to find w.

11.A group buys 4 identical entry tickets and pays a one-off booking fee of $6. The total is $46. Write an equation and calculate the cost of one ticket in NZ dollars.