1. REVIEW

2. terms
5x + 3
constant
coefficient
variable

3. Constant A number with nothing else attached to it.
Examples: 1, 2, 47, 925

4. Variable A letter that represents an unknown number.
Examples: a, b, x, y

5. Coefficient The number in front of the variable.
Examples: 3x is the coefficient
-2x is the coefficient

6. Exponent The number “on top” of the variable.
Example: x³ 3 is the exponent

7. Simplify Rewrite an expression as simply as possible.
Reducing to lowest terms.

8. Evaluate a Variable Expression
Evaluate each expression when n = 4.
a. n + 3
n + 3 = 4 + 3
= 7
b. n – 3
n – 3 = 4 – 3
= 1
Simplify (means to solve the problem or perform as many of the indicated operations as possible.)
Solution:
Substitute 4 for n. Simplify
Substitute 4 for n. Simplify
Solution:

9. Evaluate an Algebraic Expression
Evaluate each expression if x = 8.
a. 5x
5x = 5(8)
= 40
b. x ÷ 4
x ÷ 4 = 8 ÷ 4
= 2
Substitute 8 for x. Simplify
Using parenthesis is the preferred method to show multiplication. Additional ways to show multiplication are 5 · 8 and 5 x 8.
Solution:
Substitute 8 for x. Simplify
Solution:
Recall that division problems are also fractions – this problem could be written as:

10. Evaluate each expression if x = 4, y = 6, and z = 24.
a. 5xy
5xy = 5(4)(6)
= 120 b.
= 4
Substitute 4 for x; 6 for y. simplify
Solution:
Substitute 24 for z; 6 for y. Simplify.
Solution:

11. Combining Like Terms

12. Combining Like Terms
Is this a “positive 5” or “plus 5”? +5
BOTH

13. Combining Like Terms
HINT: If you don’t see a negative or positive sign in front of a number it is always positive. 5 +

14. Combining Like Terms
Is this a “negative 7” or “minus 7”? -7
BOTH

15. Combining Like Terms
“Simplify” means to combine like terms and complete all operations
2x + 2x + 3x
= 7x

16. Combining Like Terms
Terms in an expression are like terms if they have identical variable parts.
You can combine terms that are alike.

18. 4x 8x2 unlike Different types of variables are unlike terms.
To be like terms, the variable part
is what has to be the same,
not the numbers.
unlike

19. 2xy - x2y 1 unlike Different types of variables are unlike terms.
The variable part is what has
to be the same, not the numbers.
unlike

20. 3xy -9xy LIKE These are like terms even though
they contain both an x and a y.
3xy
-9xy
LIKE

21. These are also like terms.xy 1 1 yx
LIKE
We write variables in
alphabetical order.

22. xy yx LIKE 5 -3 Even if we put numbers in front
(coefficients) of each variable,
they are still like terms. xy yx
LIKE 5 -3

23. Suppose we have:
It could also be:
This is the commutative property.

24. Or:
Commutative property again

25. Like Terms – same variable with same exponent
Simplify
When combining like terms, only use the coefficients.
6x + 2x =
6x + 2x = 8x
Simplify
4x + 3y – 2x + 4y =
2x + 7y
Never, combine x’s and y’s or constant terms with variable terms.
2x + 7y ≠ 9xy and 3a + 6 ≠ 9a.

26. + 7x 7x + 3y + 3y + 5y + 5y – 9x – 9x – 17y – 17y = – 2x – 2x = – 9y
Just Watch What Happens!
+ 7x 7x
+ 3y
+ 3y
+ 5y
+ 5y
– 9x
– 9x
– 17y
– 17y
= – 2x
– 2x
= – 9y
– 9y

27. 3 + 5x = 3 + 5x ≠ 8x 3(5x) = 15x TRY THESE 1. 3q + 7q = 10q
2. 4x + 8y – 10x + 3y =
4x + 8y – 10x + 3y =
– 6x + 11y
Review Again
3 + 5x = 3 + 5x
≠ 8x
3(5x) =
15x

28. Simplify the following:
5x + 3y - 6x + 4y + 3z
5x, -6x
3y, 4y 3z
-x + 7y + 3z

33. = 6x + 5 = 3x2+ 2x + 4 = 4x2 +3x+2 Combining Like Terms

34. Like terms can be combined! Like Terms Unlike Terms
Combining Like Terms
Like terms can be combined!
Like Terms
Unlike Terms

35. Combine the following like terms.
Combining Like Terms
Combine the following like terms.
1) 3x + 5y + 4x 7x
+ 5y
2) 4a a - 2 a
+ 4

36. In algebraic terms, find the perimeter of the following shape.
4x + 3y
3x – 2y
3x – 2y 2x
To find the perimeter, add the sides together.
P = 3x – 2y + 2x + 3x – 2y + 4x + 3y =
12x – y
What is the perimeter if x = 5 and y = 8?
P = 12(5) – 8 = 52

37. Find the perimeter of the following shape when x = 2.
5x + y
5x + y
6x – 2y
To find the perimeter, add the sides together.
P = 5x + y + 5x + y + 6x – 2y =
16x = 32
Does the value of y matter in this problem?
Obviously Not!

38. A farmer has two rectangular fields.
He wants to put a fence around both. In algebraic terms, how much fence would he need?
3x – 6
2x + 5
Field 2 4
Field 1 3
P1 = x x + 5
P2 = x – 6 + 3x – 6
P1 = 4x + 16
P2 = 6x – 4
How much fence would the farmer need if x = 5?
Ptotal = 4x x – 4
Ptotal = 10x + 12
Ptotal = 10(5) + 12
Ptotal = 62