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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.

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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 ? 48 12 = 4, so r = 48.

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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

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

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EXAMPLE 2 Checking Solutions a. n – 8 = 20 SOLUTION 12 – 8 20 4 20 ≠ ANSWER 12 is not a solution. Substitute for n and then simplify.

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EXAMPLE 2 Checking Solutions b. n – 8 = 20 SOLUTION 20 = 20 28 – 8 20 28 is a solution. ANSWER Substitute for n and then simplify.

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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 = 69 + 8 Substitute. Use mental math.

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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 69. 8 + 69 77 77 = 77 ✓

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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.

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GUIDED PRACTICE for Examples 1, 2, and 3 16 plus what number equals 21 ? 16 + 5 = 21, so n = 5. 2. 16 + n = 21 Solve the equation using mental math. SOLUTION To solve an equation using mental math, think of the equation as a question.

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

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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 = 16 7 + 9 16 Tell whether the value of the variable is a solution of the equation. a = 7 4. a + 9 = 16

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GUIDED PRACTICE for Examples 1, 2, and 3 SOLUTION Tell whether the value of the variable is a solution of the equation. 5. 88 y = 8 y = 8 Substitute for y and then simplify. 11 8 ≠ 88 8 8 88 y = 8 No, 8 is not a solution. ANSWER

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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. = 1.75 + 1.25 = 3 She can do 3 loads. ANSWER = 9 ÷ 3 = 3

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EXAMPLE 2 Using the Cross Products Property 6.8 15.4 = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = 628.32 6.8 Divide.

EXAMPLE 2 Using the Cross Products Property 6.8 15.4 = 40.8 m Write original proportion. Cross products property Multiply. 6.8m 6.8 = 628.32 6.8 Divide.

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