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Equations with Variables

on Both Sides

Types of Solutions

One Solution x = a

No Solution a = b

Infinitely Many Solutions a = a

The previous lesson was solving multi-step equations. Therefore, it is assumed that students already have skills for solving these types of equations.

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Students in groups of three at the whiteboards.

First round of problems:

I will give the groups all three problems at once and ask them to solve all three and compare the types of solutions they get.

1. 3a + 2 = 3a + 7 2. 6x + 12 = 6(x + 2) 3. 6 - 7n = -2n + 3

2 = 7 No Solution 12 = 12 All Real Numbers n = ⅗

After the students work the problems, we will have a discussion about the three types of solutions and what they mean.

Second round of problems:

1. -2 + 10p = 8p - 1 2. 4(s + 2) = 4(s + 1) 3. 4p + 2 = ⅓(12p + 3) + 1

p = ½ 0 = -5 No Solution 0 = 0 All Real Numbers

Again, have a discussion about the solutions.

Third round of problems:

1. 2x - 4 = -x - 1 2. 2x - 4 = 2(x + 1) 3. 2x - 4 = 2(x - 2)

Discuss the solutions.

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Meaningful Notes

Equations with Variables on Both Sides

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Name:_______________________________________________Date:_________________Period:______________

Check Your Understanding

Equations with Variables on Both Sides: Types of Solutions

Solve each equation. Indicate if the answer is no solution, all real numbers, or one solution. If the answer is one solution, state that solution.

Show all your work. No credit will be given for solutions with no work.

1. 6(r + 2) - 4 = -10 2. 4(2a - 1) = -10(a - 5)

3. 3(1 + d) - 5 = 3d - 2 4.

5. 6. 4(2y - 1) = -8(0.5 - y)

7. 28 - 2.2x = 11.6x + 262.6 8. -0.2(1 - x) = 2(4 + 0.1x)

9. 6x + 2(x + 5) = 8x + 10 10. -2x + 10 = -3x + 2(x + 3)

1.________________

2.________________

3.________________

4.________________

5.________________

6.________________

7.________________

8.________________

9.________________

10._______________

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Name:___ANSWER KEY_______________________________Date:_________________Period:_____________

Check Your Understanding

Equations with Variables on Both Sides: Types of Solutions

Solve each equation. Indicate if the answer is no solution, all real numbers, or one solution. If the answer is one solution, state that solution.

Show all your work. No credit will be given for solutions with no work.

1. 6(r + 2) - 4 = -10 2. 4(2a - 1) = -10(a - 5)

3. 3(1 + d) - 5 = 3d - 2 4.

5. 6. 4(2y - 1) = -8(0.5 - y)

7. 28 - 2.2x = 11.6x + 262.6 8. -0.2(1 - x) = 2(4 + 0.1x)

9. 6x + 2(x + 5) = 8x + 10 10. 2x + 10 = -3x + 5(x + 3)

1. r = -3

2. a = 3

3. All Real #s

4. No Solution

5. g = -2

6. All Real #s

7. x = -17

8. No Solution

9. All Real #s

10. No solution