example 1 using mental math to solve equations a. 15 – n = 4 b. 8x = 32 c.r 12 = 4 solve the...
TRANSCRIPT
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?
48 12 = 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 – 8 20
4 20≠
ANSWER 12 is not a solution.
Substitute for n and then simplify.
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.
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.
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 ✓
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?
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.
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.
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 = 74. 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.
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
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
Laundry7.
= 1.75 + 1.25
= 3
She can do 3 loads.ANSWER
= 9 ÷ 3 = 3