The actor and director Ron Howard was born in 1954. You can use a letter such as a to represent Ron Howard’s age. When he turns a years old, the year will be 1954 + a.

The letter a has a value that can change, or vary The letter a has a value that can change, or vary. When a letter represents a number that can vary, it is called a variable. The year 1954 is a constant because the number cannot change. An algebraic expression is an expression that contains at least one variable. For example, 1954 + a is an algebraic expression.

Year born + age = year at age 16 1954 + 16 1970 18 1954 + 18 1972 21 1954 + 21 1975 36 1954 + 36 1990 a 1954 + a To evaluate an algebraic expression, substitute a number for the variable.

Example 1A: Evaluating Algebraic Expressions The expression b + 9 represents Chad’s age when his brother is b years old. Evaluate the expression for each value of b, and then tell what the value of the expression means. b = 5 b + 9 5 + 9 Substitute 5 for b. 14 Add. When his brother is 5, Chad is 14.

Example 1B: Evaluating Algebraic Expressions The expression b + 9 represents Chad’s age when his brother is b years old. Evaluate the expression for each value of b, and then tell what the value of the expression means. b = 2 b + 9 2 + 9 Substitute 2 for b. 11 Add. When his brother is 2, Chad is 11.

Check It Out! Example 1A The expression y + 7 represents Sidney’s age when her brother is y years old. Evaluate the expression for each value of y, and then tell what the value of the expression means. y = 4 y + 7 4 + 7 Substitute 4 for y. 11 Add. When her brother is 4, Sidney is 11.

Check It Out! Example 1B The expression y + 7 represents Sidney’s age when her brother is y years old. Evaluate the expression for each value of y, and then tell what the value of the expression means. y = 8 y + 7 8 + 7 Substitute 8 for y. 15 Add. When her brother is 8, Sidney is 15.

Multiplication and division of variables can be written in several ways, as shown in the table. When evaluating expressions, use the order of operations.

Example 2: Evaluating Algebraic Expressions Involving Order of Operations Evaluate the expression for the given value of the variable. A. 4x – 3 for x = 2 4(2) – 3 Substitute 2 for x. 8 – 3 Multiply. 5 Subtract.

Example 2: Evaluating Algebraic Expressions Involving Order of Operations B. s ÷ 5 + s, for s = 15 15 ÷ 5 + 15 Substitute 15 for s. 3 + 15 Divide. 18 Add. C. 5x2 + 3x, for x = 2 5(2)2 + 3(2) Substitute 2 for x. 5(4) + 3(2) Evaluate the power. 20 + 6 Multiply. 26 Add.

Check It Out! Example 2 Evaluate the expression for the given value of the variable. A. 3x – 2 for x = 3 3(3) – 2 Substitute 3 for x. 9 – 2 Multiply. 7 Subtract.

Check It Out! Example 2 B. r ÷ 3 + r, for r = 12 12 ÷ 3 + 12 Substitute 12 for r. 4 + 12 Divide. 16 Add. C. 4y2 + 2y, for y = 3 4(3)2 + 2(3) Substitute 3 for y. 4(9) + 2(3) Evaluate the power. 36 + 6 Multiply. 42 Add.

Substitute 3 for a, 2 for b, and 7 for c. + 4(2) − 7 Example 3: Evaluating Algebraic Expressions with More than One Variable 6 a Evaluate + 4b − c, for a = 3, b = 2, and c = 7. 6 a + 4b − c 6 3 Substitute 3 for a, 2 for b, and 7 for c. + 4(2) − 7 Divide and multiply from left to right. 2 + 8 − 7 Add and subtract from left to right. 3

Check It Out! Example 3 8 w Evaluate − x + 2z, for w = 2, x = 3, and z = 4 8 w − x + 2z 8 2 Substitute 2 for w, 3 for x, and 4 for z. − 3 + 2(4) Divide and multiply from left to right. 4 − 3 + 8 9 Add and subtract from left to right.