Algebraic Equations

Solving Equations by Adding and Subtracting: Vocabulary

Solve: To solve an equation mean to find a solution to the equation.

Isolate the variable: Get the variable alone on one side of the equal sign.

Addition Property of Equality: You can add the same amount to both sides of an equation, and the statement will still be true.

Vocabulary Cont…Subtraction Property of Inequality: You can

subtract the same amount from both sides of an equation, and the statement will still be true.

Inverse Operations: Operations that undo each other: addition and subtraction, multiplication and division are inverse operations of each other.

Addition Property of EqualityWords Number

sAlgebra

You can add the same amount to both sides of and the statement will still be true

2 + 3 = 5 + 4 = +4

2 + 7 = 9

x = y + z + z

x + z = y + z

Solving an Equation by AdditionSolve the equation x – 8 =

17. Check your answer.

x - 8 = 17

+ 8 + 8

x = 25

Check Your Answer:

25 - 8 = 17

17 = 17

Subtraction Property of EqualityWords Number

sAlgebra

You can subtract the same

amount from both sides of an equation and the

statement will still be true.

4 + 7 = 11

- 3 = - 3

4 + 4 = 8

8 = 8

x = y

- z = - z

x - z = y - z

Solve an Equation by SubtractionSolve the equation a + 5 =

11. Check your answer. a + 5 = 11

- 5 - 5

a = 6

Check your answer.

6 + 5 = 11

11 = 11

Solve an Equation by Addition with IntegersExample: Solve for x

x - 8 = -61. What does it mean to isolate the variable?

* Get the variable alone by moving everything else to other side of the equals sign.

2. What is the inverse operation we are going to use?*We are going to use the inverse of subtracting 8, which is adding 8

Solve an Equation by addition with Integers

x - 8 = -6 + 8 + 8

x = 2

Check your answer:

2 - 8 = -6

-6 = -6

Solve an Equation by Subtracting with IntegersExample: Solve for m

8 + m = 3

1. What does it mean to isolate the variable?* Get the variable alone by moving everything else to other side of the equals sign.

2. What is the inverse operation we are going to use?*We are going to use the inverse of adding 8, which is subtracting 8.

Solve an Equation by Subtracting with Integers

8 + m = 3

- 8 - 8

m = -5

Check your answer:

8 + -5 = 3

3 = 3

Mixed Examples1. -4 + n = 2

2. k - 15 = -20

3. 7 - a = -3

4. -29 + p = -32

Solutions:1. 6

2. -5

3. 10

4. -3

Solving Equations by MultiplyingWhat does it mean to isolate the variable?

What is the inverse operation for multiplication?

How can you use the inverse operation of multiplication to solve an equation?

Solving an Equation by MultiplyingExample: Solve for x

x = 12 7

(7) x = 12 (7) 7

x = 84

Check your answer

84 = 12 7

12 = 12

Solving an Equation by MultiplyingExample: Solve for m

m = -5 5

(5) m = -5 (5) 5

m = -25

Check your answer

-25 = -5 5

-5 = -5

Solving an Equation by DivisionWhat does it mean to isolate the variable?

What is the inverse operation for division?

How can you use the inverse operation of division to solve an equation?

Solving an Equation by DivisionExample: Solve for p

12p = 144

12p = 144 12 12

p = 12

Check your answer

12(12) = 144

144 = 144

Solving an Equation by DivisionExample: Solve for r

-9r = -81

-9r = -81 -9 -9

r = 9

Check your answer

-9(9) = -81

-81 = -81

Practice Problems8x = 96

-4m = -60

p = 3 6

n = -12 -12

12

15

18

144