1. Solving Algebraic Equations
Inverse Operations
Two-Step & Multi-Step

2. Intro to Equations
Equation - a mathematical sentence with an equal sign. It can be true, false, or open.
An equation is true if the expression on both sides of the equal sign are equal.
For example: = (TRUE)
An equation is false if the expression on both sides of the equal sign are not equal.
For example: = (FALSE)

3. Intro to Equations
When you solve, you are finding the value of the variable (Variables include = n, t, m, s, x).
You must find the value of the variable that will make both sides equal.
An equation is considered open if it contains one or more variables.
For example: x + 2 = 8
6 is a solution because when 6 is substituted in the equation for x, the equation is true.

4. Inverse Operations Inverse: opposite
When we solve equations, you must perform inverse operations, meaning whatever you do to one side of the equation, you must do to the other side to keep the equation balanced.
The inverse of adding is subtracting
Additive inverses: 12 and -12
The inverse of multiplying is dividing
Multiplicative inverses: 4 and ¼

5. Example of an Inverse Operation in an Equation
Inverse Operations
Example of an Inverse Operation in an Equation
Solve x + 5 = 33
x + 5 – 5 = 33 – 5 Undo adding 5 by subtracting 5.
x = Simplify. This isolates x.
Check x + 5 = Check your solution in the original equation.
? 33
33 = Substitute 28 for x.

6. Write the inverse of each number
Inverse Operations
Write the inverse of each number
+ 20
– 18
-72
1/6
-16/1
+ 15

7. Algebraic Equations Solve. y + 20 = 100 24 = a – 18 -72 = 9x
5z + 15 = 60