This document introduces key concepts for solving basic algebra equations using inverse operations and properties of equality. It defines variables, equations, solutions, and the processes of solving equations. It explains how to solve addition and subtraction equations by using the subtraction property of equality or addition property of equality to isolate the variable. Examples show adding or subtracting the same number from both sides of an equation to find the solution value that makes the equation true.

1. Algebra Equations
What you’ll learn in this section:
Solving equations using mental math.

2. New Vocabulary
Defining the variable: choosing a variable to
represent the unknown in a problem.
Inverse operations: operations that “undo” each
other. Addition and subtraction are inverse
operations.

3. New Vocabulary
Equation: a sentence in mathematics that contains
an equal sign.
Solution: a number that makes a sentence true.
Solving an equation: the process of finding a
solution to an equation.

4. Solve the Equation
Mentally
Solve 16 + m = 28
Solution is 12

5. Solve Mentally
1. c - 10 = 20
2. 12 = y + 8
3. 7n = 49

6. Algebra Equations
Subtraction Equation of Equality:
If you subtract the same number from both sides of
the equation, the two sides remain equal.

7. Solving Addition and
Subtraction Equations
Write the equation
x + 4 = 9

8. Solving Addition and
Subtraction Equations
Solve
x + 4 = 9
-4 - 4
Subtract 4 from both sides of
the equation

9. Solving Addition and
Subtraction Equations
Solve
x + 4 = 9
-4 - 4
x = 5
The solution is 5.
Simplify

10. Algebra Equations
Addition Property of Equality:
If you add the same number to both sides of an
equation, the two sides remain equal.

11. Algebra Equations
Write the equation
x – 13 = 25

12. Algebra Equations
x – 13 = 25
+ 13 + 13 Add 13 to both
sides of the
equation

13. Algebra Equations
x – 13 = 25
+ 13 + 13
x = 12
The solution is x = 12
Simplify

14. Algebra Equations
Your Turn
You must show your work on these problems even if
you can solve them in your head!
1. m + 15 = 34
2. n – 12 = 16
3. d + 10 = 45
4. c – 8 = 14

15. Algebra Equations
Your Turn
You must show your work on these problems even if
you can solve them in your head!
1. m + 15 = 34 m=19
2. n – 12 = 16 n = 28
3. d + 10 = 45 d = 35
4. c – 8 = 14 c = 22