Exercise Define inverse operations that undo each other

Exercise Define inverse operations that undo each other

Exercise Name two pairs of inverse operations. Addition/subtraction Multiplication/division

Exercise Explain the difference between an expression and an equation. Equations have two sides separated by an equal sign, while an expression represents a single number.

Exercise Solve x + 7 = − 16 x = − 23

Exercise Solve 9 = y − 3 y = 12

Multiplication Property of Equality For all integers a, b, and c, if a = b, then ac = bc.

Example 1 x Solve = 14 − 4 x = − 56

Example 2 Solve 9 y = 72 y=8

Example 3 Solve −n = 37 n = − 37

Example 4 Write each word phrase as a mathematical expression. Use n for the variable. a. twice a number 2 n b. four times a number 4 n c. one-third of a n or 1 n number 3 3

Example 4 Write each word phrase as a mathematical expression. Use n for the variable. d. quotient of a number and eight n or 1 n 8 8 e. quotient of eight and 8 a number n

Example 5 Write an algebraic expression for the ages of Jon and Eileen. Jon’s age is twice Joyce’s, and Eileen’s age is one-fourth of Joyce’s. Let x = Joyce’s age. Jon’s age is 2 x. 1 x Eileen’s age is x or. 4 4

Example 6 Write an equation for the sentence “Nineteen dollars is the result of dividing the cost of a tennis racket by three. ” c = 19 3

Example 7 The advertised cost for three items is $69. What is the unit price? 1. Read the sentence carefully. Choose a variable for the unknown. Let x = price per unit

Example 7 The advertised cost for three items is $69. What is the unit price? 2. The verb is indicates the equal sign. 3 x =

Example 7 The advertised cost for three items is $69. What is the unit price? 3. Place 69 to the right of the equal sign. 4. Divide both sides of the equation by 3. x = 23

Example Name the inverse operation, including the quantity, that would be used to solve each equation.

Example 9 n = 36

Example x = 12 − 4

Example 6 x + x = − 56

Example Solve.

Example z = 14 2

Example 3 n = − 51

Example − 4 m = − 6(8)

Example z = − 3 − 8

Example 7 − c = 32

Example (13 − 4)x = 108

Example − 1(13 x) = − 42 + 3

Exercise Write an equation and solve: Eighty increased by the sum of three times a number and nine is one hundred ten.

Exercise On a 627 mi. trip, Mr. Johannson traveled by airplane, automobile, and bicycle. He traveled seven times farther by plane than by car and one-seventh as far by bicycle as by car.

Exercise Write the following sum as a single fraction: n 2 n + 3

Exercise For what values of the variable or variables would 5 (a) be negative x y and (b) be positive? z