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Multi-Step Linear Equations
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Multi-Step Linear Equations
Solve multi-step linear equations using inverse operations, and check solutions by substitution.
Choose and explain
1.To begin solving 7x + 5 = 40, which operation should you perform on both sides?
- Subtract 5
- Divide by 7
- Add 5
- Multiply by 7
2.For 8x + 3 = 5x + 18, which is a useful first step to collect the variable terms on one side?
- Subtract 5x from both sides
- Subtract 3 from both sides
- Add 8x to both sides
- Divide both sides by 3
3.Select every operation that belongs in a solution of 6x − 11 = 25.
- Add 11 to both sides
- Divide both sides by 6
- Subtract 11 from both sides
- Check the value in the original equation
Solve the equations
Show your steps and keep each equation balanced.
4.Solve 5x + 9 = 34.
5.Solve 7x − 13 = 29.
6.Solve 4x + 7 = 2x + 19.
7.A skating rink charges a $6 admission fee plus $4 for each skate rental. Ethan spends $30 in all. Write an equation and find how many rentals were paid for.
Check and revise
8.Test whether x = 4 solves 3x + 8 = 20. Substitute the value and state whether the equation is true.
9.A student solves 5x + 10 = 35 by dividing every term by 5 first, writing x + 10 = 7, then x = −3. Identify the error and show the correct solution.
10.In your own words, describe a first step you can use when solving a multi-step equation and why it helps.
3 printable pages
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