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Two-Step Linear Equations
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Two-Step Linear Equations
Solve each equation using inverse operations. Show your working and check solutions by substituting them into the original equation.
Solve the Equations
Work through each equation one step at a time.
1.Solve 5x + 4 = 29. Show your steps and check your answer.
2.Solve 8y − 6 = 34. Show your steps and check your answer.
3.Solve 4a + 11 = 35. Show your steps and check your answer.
4.Solve 7b − 9 = 40. Show your steps and check your answer.
5.Solve 3m + 8 = 26. Show your steps and check your answer.
Turn Situations into Equations
Choose a variable, write an equation, and solve it.
6.Ruben has some stickers. She receives 9 more and then has 25 stickers altogether. How many stickers did she start with? Write an equation and solve it.
7.Mei saves the same amount each week for 4 weeks, then gets an extra $15. He now has $51. How much does he save each week? Write an equation and solve it.
8.A bike hire shop charges a $4 starting fee plus $3 for each hour. The total charge is $22. For how many hours was the bike hired? Write an equation and solve it.
Choose and Interpret
Select the best response for each question.
9.What should you do first to solve 6x + 7 = 31?
- Divide both sides by 6
- Subtract 7 from both sides
- Add 7 to both sides
- Multiply both sides by 6
10.Find y if 5y − 8 = 27.
- y = 5
- y = 7
- y = 19
- y = 35
11.Which equation means “a number multiplied by 5, then increased by 6, gives 31”?
- 5x − 6 = 31
- 5x + 6 = 31
- 6x + 5 = 31
- x ÷ 5 + 6 = 31
Complete and Explain
12.Complete the solution of 4x + 5 = 25: first subtract from each side to get 4x = . Then divide each side by to get x = . Check: 4( ) + 5 = .
13.In your own words, explain why doing the same operation to both sides helps keep an equation balanced. Include a short example.
14.Write a short situation that could be represented by 3n + 4 = 25. State what n represents.
15.For the situation you wrote in the previous question, solve 3n + 4 = 25 and state what your answer means.
Challenge
Take care with subtraction and with setting up a geometric equation.
16.Solve 10 − 2x = 4. Show your steps and check your answer.
17.A square has a perimeter of 30 m. Use P = 4s to write an equation and find its side length.
4 printable pages
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