Solving Equations Using Addition and Subtraction

Algebra I Section 3.1

Think of an equation as having a left and right side. Each side is on a balanced scale

x + 3 = 5

x 1 1 1 1 1 1 1 1

If I remove the 3 ones from the left side, how to I keep the scale from tipping?

A. Equivalent Equations: equations that have the same solution.

Example: x + 3 = 5 x = 5 – 3 x = 2

B. Isolating a variable: changing an equation to get the variable by itself on one side of the equation.

Example: 3 + x – 2 + (-4) = 12x = 12 – 3 + 2 + 4

1. To isolate a variable, use inverse operations2. Inverse Operations: Operations that undo each

other. The inverse of addition is ________________. The inverse of multiplication is ______________.

3. Ways to Isolate a Variablea. Add a number to both sides

x – 2 = 6

b. Subtract a number from both sides

x + 5 = 7

c. Simplify

x = 8+3

d. Change sides

6 = x

C. Solution Steps: each step you take to isolate a variable. (you must show these)

Examples:State the inverse operations1. Add 28

2. Subtract 15

Solve the equation (Show solution steps)1. X = 4 – 7

2. t – 2 = 6

3. -9 = 2 + y

4. -3 + x = 7

5. r + 3⅟4 = 2⅟2

6. |-6|+ x = 11

7. 19 – (-y) = 25

8. x + 4 – 3 = 6 • 5

9. 12 – 6 = -n

10. 4 = -b – 12

11.-r – (-7) = 16

12.Write an equation to represent the following problem. There are 15 members of a high school band brass section. After graduation there are only 7 members. How many members graduated?

• Homework– Pg 135:18-44evens

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