Algebraic Expressions

Unit 6 – Evaluating Algebraic Expressions

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

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) + 2 15 + 2 17 Yes, you have to rewrite the expression Yes, you have to use parenthesis

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

Evaluating Algebraic Expression Practice Evaluate each of the following algebraic expression x + 12 when x = 5 17 16 – y when y = 9 7 3z + 6 when z = 4 18 4. 𝑤 4 −4 when w = 20 1

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

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

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