1. Algebraic Expressions

2. Unit 6 – Evaluating Algebraic Expressions

3. Vocabulary Evaluate – to find the value of a mathematical expression.
Substitute – to replace variables in a given expression or equation with designated values in order to evaluate the expression

4. Evaluating Algebraic Expressions - Example
Evaluate each expression for the given value of the variable.
z – 13 when z = 20 z – 13 (20) – 13 7
3m + 2 when m = 5 3m + 2 3(5)
Yes, you have to rewrite the expression
Yes, you have to use parenthesis

5. Evaluating Algebraic Expressions - Example
Evaluate each expression for the given value of the variable.
40 – 5p when p = 6 40 – 5p 40 – 5(6) 40 – 30 10
2𝑑 9 when d = 3
𝟐𝒅 𝟗
𝟐(𝟑) 𝟗
𝟔 𝟗
𝟐 𝟑

6. Evaluating Algebraic Expression Practice
Evaluate each of the following algebraic expression
x when x = 5 17
16 – y when y = 9 7
3z + 6 when z = 4 18
4. 𝑤 4 −4 when w = 20 1

7. Evaluating Algebraic Expressions - Example
Write each verbal expression as a variable expression and then evaluate each of the following when x = 3
The sum of 6x and 4
6x + 4
6(3) + 4
18 + 4 22
12 less than 7x
7x - 12
7(3) – 12
21 – 12 9

8. Evaluating Algebraic Expressions - Example
Write each verbal expression as a variable expression and then evaluate each of the following when x = 3
The product of
(5 + 3x) and (2x – 3)
(5 + 3(3)) × (2(3) – 3)
(5 + 9) × (6 – 3)
14 × 3 42
The quotient of
(4x – 5) and (5x – 1)
4𝑥 −5 5𝑥 −1
4 3 −4 5 3 −1
12 −4 15 −1
7 14
𝟏 𝟐

9. Evaluating Algebraic Expression Practice
Write an algebraic expression for each of the following verbal expressions. Then use the value of the variable to evaluate the expression.
A number that is 5 more than twice x when x = 2
2x + 5 9
The total cost of 4 pencils and 5 pens if each pencil costs w cents and each pen costs 2w cents when w = $0.25
4w + 5(2w)
$3.50
The length of a side of a square whose perimeter is r units when r = 28 inches
𝒓 𝟒
7 inches
The perimeter of a rectangle whose sides are lengths of (3z + 2) and (2z + 3) units when z = 5
2(3z + 2) + 2(2z + 3)
60 units