Solving Equations UsingAddition or Subtraction

Objective:Students will solve linear equations using addition and subtraction.

8.EE.7 Solve Linear Equations in one variable

Algebra Standards:

Vocabulary

Equivalent equations:

Inverse operations:

Linear equation:

are equations that have the same solution(s).

are operations that undo each other, such asaddition and subtraction.

The exponent of the variable(s) is one.

Equation - a balanced statement of equalitybetween two quantities.

4 + 3 = 7

fulcrum

4 + 3 7=

What is an Equation?

4 + 3 7=- 3 - 3

What is an Equation?

4 4=

Perform the same operation to both sides to keep the equation balanced.

What is an Equation?

x + 6 11=

This property can be used to solve variable equations.

-6 -6

x 5=

x + 6 = 11-6 -6x

Algebraic Approach

What is an Equation?

0

= 5

Operation Original Equation Equivalent Equation

• Add the samenumber to each side

• Subtract the same numberfrom each side

• Simplify one or both sides

Transforming Equations

x – 3 = 5

x + 6 = 10

x = 8 – 3

Add ___

Subtract ___

Simplify

x = ___

x = ___

x = ____

3 8

6 4

5

#1 Add to Each side of an Equation

Solve x – 9 = -20 +9 +9

x 11 - =

0

#2 Simplify first

Solve n – (-8) = -2

-8 -8n 10 -

n +

8= -2

=

0

Check Point: Solve the equation.

1) x – 7 = -15 2) n – (-6) = 4

4) 5 – (-z) = 21 3) -7 = 10 + y

+7 +7x 8 - -6 -6

n 2 -

n +6= 4

-10 -10 y 17 - -5 -5

z 16

5 +z = 21

=

=

= =

0

0

0

0

Check Point: Solve the equation.

5) m – (-3) = 14

-3 -3m 11

m + 3= 14

6) -8 = -b + (-2)+2 +2

-b 6 -

-1 -1-6 = (-1)b

b 6

=

=

=

0

0

1