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Two-Step Linear Equations
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Two-Step Linear Equations
Solve each equation by undoing operations in reverse order. Show your working where space is provided. When checking, substitute your value into the original equation.
Recognising the steps
1.Select every equation that needs two inverse operations to isolate the variable.
- 5a + 4 = 29
- b - 8 = 13
- 3c = 24
- 7d - 6 = 22
- e + 9 = 16
2.For 6p - 11 = 31, name the two operations you would use to isolate p, in the order you would use them.
3.Which operation should you undo first in 8q + 5 = 45?
- Subtract 5 from both sides
- Add 5 to both sides
- Divide both sides by 8
- Multiply both sides by 8
Solve and show your working
4.Solve 4x + 7 = 35.
5.Solve 5y - 12 = 23.
6.Solve 3m + 14 = 41.
7.Solve 7n - 18 = 31.
Check by substitution
8.Test whether x = 6 makes 4x - 3 = 21 true. Substitute 6 for x and decide whether the two sides are equal.
9.Test whether y = 5 satisfies 3y + 8 = 25. Show the substitution and state whether the value works.
10.Solve 6r + 4 = 46, then check your answer by substituting it into the original equation.
Equations in context
11.A bike hire shop charges a fixed fee of $8 plus $6 for each hour. Maia pays $38 altogether. Write an equation and work out how many hours she hired the bike.
12.Harrison had some money. After buying a $9 snack, he had $27 left. Write and solve an equation to find how much money he had before buying the snack.
13.Number the two solving operations in the order you would use them to solve 9t - 5 = 58. Write 1 or 2 beside each operation.
14.In your own words, describe a reliable order for solving a two-step equation such as 2w + 9 = 25.
3 printable pages
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