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Two-Step Algebraic Equations
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Two-Step Algebraic Equations
Undo operations in reverse order to solve. Show your working, and check solutions by substituting them into the original equation.
Understanding equations
1.Select every equation below that requires two inverse-operation steps to isolate the variable.
- m + 9 = 16
- 3p + 4 = 19
- 7q = 35
- 5r − 6 = 24
- t − 8 = 11
2.In an equation, what does the equals sign tell you about the expressions on its two sides?
3.Complete the inverse-operation pairs: subtraction is the inverse of ; division is the inverse of .
Solve and check
Use inverse operations to find each variable. Show your steps.
4.Solve 4x + 3 = 27.
5.Solve 5y − 7 = 18.
6.Solve 3a + 8 = 29.
7.Solve 6b − 5 = 31.
8.Test the value x = 4 in 3x + 2 = 14. Substitute it into the left side, then decide whether it is a solution.
TrueFalse
9.Test y = 3 in 4y − 1 = 10. Substitute it into the left side, then decide whether it is a solution.
TrueFalse
10.Which value solves 7x + 2 = 37?
- x = 3
- x = 4
- x = 5
- x = 6
Equations in context
11.Tui has some marbles. She gives 5 away, then shares the rest equally between 4 cousins. Each cousin receives 6 marbles. Let m be her starting number. Write an equation and work out m.
12.A bike hire shop charges a $4 booking fee plus $3 for each hour. The total cost is $22. Let h be the number of hours. Write an equation and find h.
Challenge
13.Match each equation to its solution.
- 2x + 8 = 20
- 3y − 4 = 17
- 4a + 5 = 33
- 5b − 9 = 21
- b = 6
- x = 6
- a = 7
- y = 7
14.Write a two-step equation with solution n = 4. Then show how to solve it.
15.Explain how to solve an equation such as 2x + 5 = 17. Include the order of inverse operations and why you use them.
3 printable pages
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