Solving Equations Using Addition and Subtraction Algebra I Section 3.1

Think of an equation as having a left and right side 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) = 12 x = 12 – 3 + 2 + 4 To isolate a variable, use inverse operations Inverse Operations: Operations that undo each other. The inverse of addition is ________________. The inverse of multiplication is ______________.

x – 2 = 6 x + 5 = 7 x = 8+3 6 = x Ways to Isolate a Variable a. 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 C. Solution Steps: each step you take to isolate a variable. (you must show these) Examples: State the inverse operations Add 28 Subtract 15

Solve the equation (Show solution steps) X = 4 – 7 t – 2 = 6 -9 = 2 + y

-3 + x = 7 r + 3⅟4 = 2⅟2 |-6|+ x = 11

19 – (-y) = 25 x + 4 – 3 = 6 • 5 12 – 6 = -n

4 = -b – 12 -r – (-7) = 16 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 www.buckalgebra.wikispaces.com