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Solving Equations Algebraically

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Solving Equations Algebraically

A verbal model explains the steps needed to solve the equation. In your mind you should always think the verbal model.

FBS = from both sides

Example #1:

5x + 8 = 8x + 2

-5x-5x

8 = 3x + 2

-2 -2

6 = 3x

3 3

2 = x

Verbal Model:

1. Take 5x FBS

2. Take 2 FBS

3. Split into 3 groups

Example #2:

10x + 2 = 6x + 14

-6x-6x

4x + 2= + 14

-2 -2

4x= 12

4 4

x = 3

Verbal Model:

1. Take 6x FBS

2. Take 2 FBS

3. Split into 4 groups

Example #3:

2(5x + 3) = 6(x + 3)

10x + 6 = 6x + 18

-6x-6x

4x + 6= + 18

-6 -6

4x= 12

4 4

x = 3

Verbal Model:

1. Distribute

2. Take 6x FBS

3. Take 6 FBS

4. Split into 4 groups

- Example #4:
- 4(2x + 4) = 2(5x + 3)

8x + 16 = 10x + 6

-8x -8x

16 = 2x + 6

-6 -6

10= 2x

2 2

5 = x

Verbal Model:

1. Distribute

2. Take 8x FBS

3. Take 6 FBS

4. Split into 2 groups

Example #5:

2(3x + 4) = 4(x + 4)

6x + 8 = 4x + 16

-4x -4x

2x +8= + 16

-8 -8

2x= 8

2 2

x = 4

Verbal Model:

1. Distribute

2. Take 4x FBS

3. Take 8 FBS

4. Split into 2 groups

Example #6:

5(x + 3) + 3(2x + 1) = 8(x + 2) + 8

5x + 15 + 6x + 3 = 8x + 16 + 8

11x + 18 = 8x + 24

-8x -8x

3x + 18 = + 24

-18 -18

3x= 6

3 3

x = 2

Verbal Model:

Distribute

2. Combine like terms

3. Take 8x FBS

4. Take 18 FBS

5. Split into 3 groups