REVIEW

terms 5x + 3 constant coefficient variable

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

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

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

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

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

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:

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:

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:

Combining Like Terms

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

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

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

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

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

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

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

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

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

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

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

Or: Commutative property again

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.

+ 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

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

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

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

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

Combine the following like terms. Combining Like Terms Combine the following like terms. 1) 3x + 5y + 4x 7x + 5y 2) 4a + 6 - 3a - 2 a + 4

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

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!

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 = 3 + 3 + 2x + 5 + 2x + 5 P2 = 4 + 4 + 3x – 6 + 3x – 6 P1 = 4x + 16 P2 = 6x – 4 How much fence would the farmer need if x = 5? Ptotal = 4x + 16 + 6x – 4 Ptotal = 10x + 12 Ptotal = 10(5) + 12 Ptotal = 62