1.3 Algebraic Expressions

Modeling words with an Algebraic Expression:

Example 1: Multiple Choice Which algebraic expression models the phrase "seven fewer than a number t"?

A) -7t B) 7 - t C) t - 7 D) 7 + t

Example 2: Multiple Choice Which algebraic expression models the phrase "two times the sum of a and b"?

F) a + b G) 2a + b H) 2(a + b) I) a + 2b

Modeling a Situation:

Example 3: You start with $20 and save $6 each week. What algebraic expression models the total amount you save?

Example 4: You had $150, but you are spending $2 each day. What algebraic expression models this situation?

1 Evaluating Algebraic Expressions: Example 5: What is the value of the expression for the given values of the variables? a. 7(a + 4) + 3b - 8 for a = -4 and b = 5

b.

c.

2 Writing and Evaluating Algebraic Expressions:

Example 6: In football, a touchdown (TD) is worth six points, and extra-point kick (EPK) one point, and a field goal (FG) three points. a. What algebraic expression models the total number of points that a football team scores in a game, assuming each scoring play is one of the three given types? Let t = the number of touchdowns Let k = the number of extra-point kicks Let f = the number of field goals

b. Suppose a football team scores 3 touchdowns, 2 extra-point kicks, and 4 field goals. How many points did the team score?

3 Example 7: In basketball, teams can score by making two-point shots, three-point shots, and one-point free throws. a. What algebraic expression models the total number of points that a basketball team scores in a game, assuming each scoring play is one of the three given types? Let x = the number of two-point shots Let y = the number of three-point shots Let z = the number of free throws

b. If a team makes 10 two-point shots, 5 three-point shots, and 7 free throws, how many points do they score in all?

4 Vocabulary:

5 Simplifying Algebraic Expressions:

Example 8: Combine like terms to find the simpler form of each expression. a. b.

c. d.

6