Main Idea and New Vocabulary Example 1: Identify Parts of an Expression Example 2: Simplify Algebraic Expressions Example 3: Simplify Algebraic Expressions Example 4: Real-World Example Lesson Menu

Simplify algebraic expressions. term coefficient like terms constant Main Idea/Vocabulary

Identify Parts of an Expression Identify the terms, like terms, coefficients, and constants in the expression 3x – 5 + 2x – x. 3x – 5 + 2x – x = 3x + (–5) + 2x + (–1x) Rewrite the expression. Answer: • terms: 3x, –5, 2x, and –x • like terms: 3x, 2x, and –x • coefficients: 3, 2, and –1 • constant: –5 Example 1

Identify the terms, like terms, coefficients, and constants in the expression n – 4 + 7n – 6n. A. terms: n, –4, 7n, –6n; terms: like terms: n and 7n; coefficients: 1, 7, and –6; constant: –4 B. terms: n, –4, 7n, –6n; like terms: n, 7n, and –6n; coefficients: 1, 7, and –6; constant: –4 C. terms: n, 4, 7n, 6n; like terms: n, 7n, and –6n; coefficients: 1, –4, 7, and –6; constant: –4 D. terms: n, 4, 7n, 6n; like terms: n, 7n, and –6n; coefficients: 1, –4, 7, and –6; constant: none Example 1 CYP

Simplify Algebraic Expressions Write the expression 6n – n in simplest form. 6n and n are like terms. 6n – n = 6n – 1n Identity Property; n = 1n = (6 – 1)n Distributive Property = 5n Simplify. Answer: 5n Example 2

Write the expression 10w + w in simplest form. A. 10w B. 11w C. 10w + 1 D. 10 + w Example 2 CYP

Simplify Algebraic Expressions Write the expression 8z + z – 5 – 9z + 2 in simplest form. 8z, z, and –9z are like terms. –5 and 2 are also like terms. 8z + z – 5 – 9z + 2 = 8z + z + (–5) + (–9z) + 2 Definition of subtraction = 8z + z + (–9z) + (–5) + 2 Commutative Property = [8 + 1 + (–9)]z + (–5) + 2 Distributive Property Example 3

Simplify Algebraic Expressions = 0z + (–3) Simplify. = 0 + (–3) or –3 0z = 0 • z or 0 Answer: –3 Example 3

Write the expression 4t + 3 – t + 7 in simplest form. A. 5t + 10 B. 4t – 4 C. 3t + 10 D. 3t – 4 Example 3 CYP

GROCERIES Manfred buys some boxes of cereal for $4 GROCERIES Manfred buys some boxes of cereal for $4.85 each and the same number of bags of pretzels for $2.90 each. Write an expression in simplest form that represents the total amount spent. Example 4

4.85x + 2.90x = (4.85 + 2.90)x Distributive Property = 7.75x Simplify. Answer: The expression $7.75x represents the total amount spent. Example 4

MOVIES Each person in a group buys a movie ticket for $7 MOVIES Each person in a group buys a movie ticket for $7.50 and a tub of popcorn for $3.80. Write an expression in simplest form that represents the total amount spent. A. $11.30 B. $11.30x C. $7.50x + $3.80 D. $7.50 + $3.80 + x Example 4 CYP