1. Algebraic Expressions

2. Warm Up
Change to a Percent
Simplify

3. Like Terms
Term- a number, variable, or product of a number and one or more variables
Ex.: 3a – 4b + 5 has 3 terms
Like Terms- terms with the same variables and the same exponents
Ex.: 2x, 3x
4mn, 12mn
In the term 3a, 3 is called
the numerical coefficient
Note:
and are
NOT like terms

4. Simplify

5. Simplify

6. Simplify

7. Solving Equations

8. Solving Equations
In this section we are going to learn how to solve linear (or first degree) equations.
A linear equation is one in which the exponent on the variable is 1.
Example: 5x – 1 = 3
2x + 4 = 6x - 5

9. Equivalent Equations
Equivalent Equations are equations that have the same solution.
The following are equivalent equations:
2x – 5 = 1
2x = 6
x = 3

10. When we solve an equation, we write the equation as a series of simpler equivalent equations until we obtain an equation of the form x = c, where c is some real number.

11. Isolate the Variable
To solve any equation, we have to isolate the variable.
That means getting the variable by itself on one side of the equals sign.
There are 4 properties we will use to isolate the variable.

12. Addition Property of Equality
You can add the same number to both
sides of an equation and the equation
remains equivalent.

13. Example:

14. Subtraction Property of Equality
You can subtract the same number to both
sides of an equation and the equation
remains equivalent.

15. Example:

16. Multiplication Property of Equality
You can multiply the same number on both
sides of an equation and the equation
remains equivalent.

17. Example:

18. Division Property of Equality
You can divide the same number on both
sides of an equation and the equation
remains equivalent.

19. Example:

20. Procedure to Solve Equations
1. Get rid of fractions.
2. Distribute when needed.
3. Combine like terms on same side of equals.
Use the addition/subtraction property. You
may have to use it more than once!
Solve using either the multiplication property
or the division property.

21. Solve

22. Solve

23. Solve

24. Variables on Both Sides
Your goal is to get the variable on one side of the equals sign and everything else on the other side of the equals sign.
Always combine like terms on each side of the equation FIRST!

25. Example:

26. Solve

27. Solve

28. Grouping Symbols
You have to distribute before
you combine like terms.

29. Solve

30. Solve