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Two-Step Linear Equations
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Two-Step Linear Equations
Solve each equation by keeping both sides balanced. Show your working where space is provided. Use NZ dollars where relevant.
Recognising and undoing operations
1.Which equation has two operations applied to the variable?
- x + 11 = 18
- 5p = 35
- 4a − 6 = 22
- t ÷ 3 = 8
2.In 6r + 7 = 31, name the two operations applied to r.
3.What should you undo first when solving 6r + 7 = 31?
- Add 7
- Subtract 7
- Multiply by 6
- Divide by 6
Solve the equations
4.Solve 4x + 9 = 29. Give the value of x.
5.Solve 7y − 5 = 30. Give the value of y.
6.Solve 3m + 14 = 35. Give the value of m.
7.Solve 5n − 12 = 23. Give the value of n.
Check by substitution
8.Test whether x = 6 satisfies 4x − 3 = 17. Substitute the value and decide if the equation is true.
TrueFalse
9.Test whether p = 8 satisfies 3p + 2 = 25. Substitute the value and decide if the equation is true.
TrueFalse
10.Solve 5k + 4 = 39, then check your solution by substituting it into the original equation.
Equations in everyday situations
11.A group orders 4 identical lunch boxes and pays a $6 delivery charge. The total is $38. Write an equation and find the price of one lunch box.
12.A bike hire shop charges $5 per hour plus a $4 helmet fee. The bill is $29. Write an equation and work out how many hours the bike was hired.
13.A number is doubled, then 9 is added. The result is 31. Write an equation and find the number.
Challenge
14.Solve 8x − 6 = 3x + 19.
15.Solve 4(y + 3) = 28.
16.Find the missing constant in 3x + □ = 26 if x = 6.
17.Describe a reliable order of steps for solving an equation such as 5x + 8 = 33.
4 printable pages
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