EXAMPLE 1 Using Mental Math to Solve Equations a. 15 – n = 4 b. 8x = 32 c.r 12 = 4 Solve the equation using mental math.

EXAMPLE 1 Using Mental Math to Solve Equations SOLUTION To solve an equation using mental math, think of the equation as a question. a. 15 minus what number equals 4 ? 15 – 11 = 4, so n = 11. b. 8 times what number equals 32 ? 8(4) = 32, so x = 4. c. What number divided by 12 equals 4 ? = 4, so r = 48.

GUIDED PRACTICE for Examples 1, 2, and 3 Tell whether the value of the variable is a solution of the equation. 6. 7n = 13 n = 2 No, 2 is not a solution. ANSWER

EXAMPLE 2 Checking Solutions a. n = 12 b. n = 28 Tell whether the value of the variable is a solution of n – 8 = 20.

EXAMPLE 2 Checking Solutions a. n – 8 = 20 SOLUTION 12 – ≠ ANSWER 12 is not a solution. Substitute for n and then simplify.

EXAMPLE 2 Checking Solutions b. n – 8 = 20 SOLUTION 20 = – is a solution. ANSWER Substitute for n and then simplify.

EXAMPLE 3 Writing an Equation Times Square The Times Square New Year’s Eve Ball drops a total of 77 feet in 60 seconds. After 54 seconds it has dropped 69 feet. How many more feet will it drop? SOLUTION You can use a verbal model to write an equation. Let d represent the distance left to drop. 77 = 69 + d Write a verbal model. 77 = Substitute. Use mental math.

EXAMPLE 3 Writing an Equation Because d = 8, the ball will drop 8 more feet. ANSWER Check You can check your answer by finding the sum of 8 and = 77 ✓

GUIDED PRACTICE for Examples 1, 2, and 3 Solve the equation using mental math. 1. 5x = 45 SOLUTION To solve an equation using mental math, think of the equation as a question. 5 times what number equals 45 ? 5(9) = 45, so x = 9.

GUIDED PRACTICE for Examples 1, 2, and 3 16 plus what number equals 21 ? = 21, so n = n = 21 Solve the equation using mental math. SOLUTION To solve an equation using mental math, think of the equation as a question.

GUIDED PRACTICE for Examples 1, 2, and 3 What number divided by 6 equals 9 ? 54 6 = 9, so r = t 6 = 9 Solve the equation using mental math. SOLUTION To solve an equation using mental math, think of the equation as a question.

GUIDED PRACTICE for Examples 1, 2, and 3 SOLUTION 16 = 16 ANSWER Yes, 16 is a solution. Substitute for a and then simplify. a + 9 = Tell whether the value of the variable is a solution of the equation. a = 7 4. a + 9 = 16

GUIDED PRACTICE for Examples 1, 2, and 3 SOLUTION Tell whether the value of the variable is a solution of the equation y = 8 y = 8 Substitute for y and then simplify ≠ y = 8 No, 8 is not a solution. ANSWER

GUIDED PRACTICE for Examples 1, 2, and 3 Julie has $9 to wash her clothes at the laundromat. Each load costs $1.75 to wash and $1.25 to dry. How many loads can she do? SOLUTION Laundry 7. = = 3 She can do 3 loads. ANSWER = 9 ÷ 3 = 3

EXAMPLE 4 Standardized Test Practice SOLUTION STEP 1 Write and solve an equation to find Cesar’s height. Cesar’s height – Marco’s height = 5 Write a verbal model.

EXAMPLE 4 Standardized Test Practice STEP 1 c – 50 = 5 Substitute 50 for Marco’s height. Use mental math. 55 – 50 = 5 Cesar is 55 inches tall.

EXAMPLE 4 Standardized Test Practice STEP 2 Use Cesar’s height to find Luis’s height. Add: = 58. ANSWER Luis is 58 inches tall. The correct answer is D.

GUIDED PRACTICE for Example 4 8. What If? In Example 4, suppose Luis is 3 inches taller than Marco, Cesar is 50 inches tall, and the difference of Cesar’s and Marco’s height is 5 inches. How tall is Luis? SOLUTION STEP 1 Write and solve an equation to find Cesar’s height. Cesar’s height – Marco’s height = 5 Write a verbal model.

GUIDED PRACTICE for Example 4 STEP 1 50 – m = 5 Substitute 50 for Cesar’s height. Use mental math. 55 – 50 = 5 Marco’s is 45 inches tall.

GUIDED PRACTICE for Example 4 STEP 2 Use Marco’s height to find Luis’s height. Add: = 48. ANSWER Luis is 48 inches tall.