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One-Step Linear Equations

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One-Step Linear Equations

Solve each equation by undoing the operation on the variable. Keep both sides balanced, and show your working where space is provided.

Understand the equation

An equation states that the expressions on its two sides have equal value.

1.In an equation, what does the equals sign tell you?
  • The value on the left is the same as the value on the right
  • The numbers should always be added
  • The calculation is finished
  • The variable must be zero
2.Select every equation that can be solved in one step because it has one variable with a single addition or subtraction operation.
  • a + 6 = 14
  • 3b + 2 = 17
  • c − 8 = 5
  • 21 = d + 13
  • 4m + 2n = 18

Equations with addition

Undo addition by subtracting the same amount from both sides.

3.Solve: x + 11 = 18
4.Solve: 8 + y = 19
5.Solve: r + 14 = 25
6.Substitute your solution into the original equation to check it: x + 11 = 18. Show the substitution and verify both sides are equal.

Equations with subtraction

Undo subtraction by adding the same amount to both sides.

7.Solve: m − 7 = 12
8.Solve: p − 13 = 6
9.Solve: 20 = n − 9
10.To solve x − 18 = 27, which operation should you apply to both sides first?
  • Add 18
  • Subtract 18
  • Multiply by 18
  • Divide by 18

Equations in everyday situations

Choose a variable for the unknown, write an equation, and solve it.

11.Kahu has $9 and then earns some more money. She now has $24. Let e be the amount she earned. Write an equation and find e.
12.Wiremu had some trading cards. After giving 9 cards to a friend, he had 16 left. Let c be the number he started with. Write an equation and find c.
13.A netball team scored 17 points in the first quarter and some points in the second quarter. Their combined score was 31 points. Let q be the second-quarter score. Write an equation and find q.
14.At sunrise, the temperature was t degrees Celsius. It rose by 6°C to reach 21°C. Write an equation and find the sunrise temperature.

Mixed practice

15.Match each equation to its solution.
  • a + 5 = 13
  • b − 6 = 9
  • 22 = k + 6
  • w − 4 = 12
  • w = 16
  • b = 15
  • k = 16
  • a = 8
16.Complete the solution for x + 12 = 20: 12 from both sides; then x = 20 12; finally, x = .
17.Explain why doing the same operation to both sides of an equation helps keep the equation true.
18.A student solves y − 5 = 14 and gets y = 9. Is the solution correct? Substitute y = 9 into the original equation and explain your decision.

4 printable pages

  • One-Step Linear Equations, page 1 of 4: Understand the equation, Equations with addition

    Page 1

  • One-Step Linear Equations, page 2 of 4: Equations with subtraction

    Page 2

  • One-Step Linear Equations, page 3 of 4: Equations in everyday situations

    Page 3

  • One-Step Linear Equations, page 4 of 4: Mixed practice

    Page 4

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