Main Idea and New Vocabulary Example 1 Identify

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

• Simplify algebraic expressions. • term • coefficient • like terms • constant

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

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

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

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

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

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

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

4. 85 x + 2. 90 x = (4. 85 + 2. 90)x = 7. 75 x Distributive Property Simplify. Answer: The expression $7. 75 x represents the total amount spent.

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. 30 x C. $7. 50 x + $3. 80 D. $7. 50 + $3. 80 + x