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One-Step Linear Equations

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One-Step Linear Equations

Solve each equation by using the inverse operation on both sides. Show working where space is provided. Check solutions by substituting them into the original equation.

Understanding equations

1.In an equation, what does the equals sign tell you? Choose the best description.

The expression on the left has the same value as the expression on the right
The answer must be written after the sign
The numbers should be added together
The variable has a value of zero

2.Select every equation below that can be solved in one step.

a + 8 = 21
4b = 28
c − 6 = 13
3d + 2 = 17
e ÷ 5 = 4

Equations with addition

3.Find x: x + 9 = 23.

4.Find r: r + 16 = 31.

5.Find k: k + 7 = 19.

6.Solve x + 9 = 23 by substituting your value of x into the original equation. Show that both sides are equal.

Equations with subtraction

7.Find y: y − 8 = 11.

8.Find t: t − 13 = 6.

9.Find p: p − 5 = 17.

10.To isolate n in n − 12 = 20, which operation should you apply to both sides?

Subtract 12
Add 12
Multiply by 12
Divide by 12

Equations in context

11.Keira has $9 and then earns some money. She now has $24. Write an equation and work out how much she earned.

12.A netball team scores some goals in the first quarter and 12 goals in the second quarter. Their combined score is 29 goals. How many goals did they score in the first quarter? Write an equation and solve it.

13.Harrison has 32 trading cards and gives some away. He has 21 cards left. How many cards did he give away? Write an equation and solve it.

Mixed practice and reasoning

14.Match each equation to its solution.

a + 11 = 18
b − 9 = 8
c + 6 = 22
d − 7 = 10

b = 17
a = 7
c = 16
d = 17

15.Complete the solution: To solve q + 8 = 20, first 8 from both sides. Then q = 20 8, so q = .

16.Solve 3x = 27. Then check your value by substituting it into the equation.

17.In your own words, explain what it means to solve an equation. Include what you are trying to find.

18.Why can substituting a solution into the original equation help you check your work?

19.A bus fare is the same for each passenger. The total fare for one passenger plus a $3 booking fee is $8. Write an equation and find the passenger fare.