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Linear Equations Practice
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Linear Equations Practice
Solve each equation. Show your working and check solutions by substituting them back into the original equation. Use the NZ dollar symbol where needed.
One-step equations
1.Solve m + 9 = 16. Then check your value of m.
2.Solve 4p = 28. Check your solution in the equation.
3.Find n if n − 6 = 11. Show a check.
4.Solve q ÷ 5 = 3. Verify your answer.
5.Solve r + 13 = 22, and check the result.
Two-step and variable-on-both-sides equations
6.Solve 3x + 4 = 19. Show the inverse operations and check your answer.
7.Find a if 5a − 7 = 18. Check by substitution.
8.Solve 2b + 9 = 25, then substitute your answer to check.
9.Solve 6c − 8 = 4. Include a check.
10.Challenge: solve 2d + 7 = d + 15. Check the value you find.
Turn situations into equations
11.Manaia had some marbles. She gave 9 away and now has 18. Let k be the number she had at first. Write an equation and solve it.
12.A bike hire costs $4 to start, plus $3 for each hour. The total charge is $19. Let h be the number of hours. Write an equation and work out h.
13.Wiremu buys 3 identical notebooks and pays $5 for delivery. The whole order costs $29. Let c be the cost of one notebook. Write an equation and find c.
Recognising and checking equations
14.Select every linear equation in this list.
- 4x − 3 = 13
- y² + 1 = 10
- 7z = 42
- 12 ÷ p = 3
- 2a + 8 = 20
15.What does the equals sign tell you in 3x + 2 = 14?
- The left side is greater than the right side.
- The two sides have the same value.
- The left side should be multiplied by the right side.
- The equation is asking for addition only.
16.Match each equation to the inverse operation that helps undo the operation on the variable first.
- u + 8 = 17
- 5v = 30
- w − 6 = 10
- t ÷ 4 = 7
- Multiply by 4
- Add 6
- Subtract 8
- Divide by 5
Explain and create
17.Describe a reliable order for solving an equation such as 4x − 3 = 17.
18.Explain how substituting a solution back into an equation can show whether the solution is correct. Use 2x + 1 = 11 as an example.
19.Create a word problem with a whole-number answer that can be represented by 3x + 4 = 22. Write the equation and give its solution.
5 printable pages
Page 1
Page 2
Page 3
Page 4
Page 5
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