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Multi-Step Linear Equations
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Multi-Step Linear Equations
Expand brackets carefully, collect like terms, and keep equations balanced by doing the same operation to both sides. Show your working and check solutions by substitution.
Expand brackets
Use the distributive property to remove each set of brackets.
1.Expand 4(x + 6).
2.Expand 3(2x − 5).
3.Expand −2(x − 8).
4.Which expression is equivalent to 5(x − 3)?
- 5x − 3
- 5x − 15
- 5x + 15
- x − 15
Solve multi-step equations
Solve each equation. Show the steps you use to isolate x.
5.Solve 3x + 8 = 26.
6.Solve 4x − 7 = 21.
7.Solve 7x + 5 = 3x + 29.
Equations with brackets
Expand first, then simplify and solve.
8.Solve 3(x + 2) = 21.
9.Solve 4(x − 3) = 20.
10.Solve 2(3x + 1) = x + 17.
11.Select every good practice when solving a multi-step equation.
- Expand brackets when needed
- Combine like terms
- Apply the same operation to both sides
- Substitute the result into the original equation to check it
- Ignore negative signs to make the work quicker
Check solutions
12.Test whether x = 4 satisfies 3(x + 2) = 21. Substitute 4 into the left side, evaluate it, and compare it with the right side. Is x = 4 a solution?
13.Solve 4(x − 1) + 6 = 22, then check your result by substituting it into the original equation.
Use equations in context
14.Losa has $38 saved and puts aside $15 each week. How many weeks will it take for her savings to reach $158? Write an equation and solve it.
15.A rectangle is 5 cm longer than twice its width. Its perimeter is 46 cm. Find its width. Write an equation and solve it.
Challenge
16.Solve 4(2x − 3) − 3(x + 2) = 17.
17.Match each equation with its solution.
- 2(x + 4) = 18
- 5(x − 1) = 20
- 3(x + 2) = 15
- x = 5
- x = 5
- x = 3
4 printable pages
Page 1
Page 2
Page 3
Page 4
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