Algebra 1 2-4 Guided Practice: Solving Equations with Variables on Both Sides

by Matthew Richardson

| 17 Questions1

2

1

10

Solve It! The diagram gives information about the populations of two towns. After how many years will the populations be equal?

Enter only a number.

2

10

Solve It! Explain how you found your response to the previous item.

3

3

10

Take Note: Correctly order the steps below to describe the process (so far) for solving an equation with variables on both sides of the equation.

- Combine like terms and use inverse operations to isolate the variable.
- Check your solution by substituting it into the original equation.
- Work to get the variables together on the same side of the equation and the constants on the other.

4

10

Problem 1 Got It? What is the solution of the equation?

Show your work on the canvas.

You may also complete your work on paper or on a whiteboard and upload a clear picture of it to the canvas.

-4

3

-6

12

5

5

10

Problem 1 Got It? Solve the equation from problem 1 by first subtracting 5x from each side instead of 2x. Do you get the same solution?

No, subtracting 5x yields a different solution.

Yes, 22 is the solution either way.

6

6

10

Problem 2 Got It? An office manager spent $650 on a new energy-saving copier that will reduce the monthly electric bill for the office from $112 to $88. In how many months will the copier pay for itself?

A

B

C

D

7

7

10

Problem 3 Got It?

A

B

C

D

8

8

10

Problem 3 Got It?

A

B

C

D

9

10

11

12

13

9

10

Take Note: Describe what makes and equation an identity.

10

5

Take Note: Provide an example equation that has only one solution.

11

5

Take Note: Provide an example equation that has no solution.

12

5

Take Note: Provide an example equation that is an identity.

13

5

Take Note: How many solutions do identities have?

infinitely-many

zero

one

three

two

14

14

10

Problem 4 Got It?

A

B

C

D

15

15

10

Problem 4 Got It?

A

B

C

D

16

10

Take Note: Place the five steps for solving equations in chronological order.

- Combine like terms on each side of the equation.
- Use the properties of equality to solve for the variable.
- Check your solution in the original equation.
- Use the properties of equality to get the variable terms on one side of the equation and the constants on the other.
- Use the Distributive Property to remove any grouping symbols. Use properties of equality to clear decimals and fractions.

17

17

10

Take Note: Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

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