chapter1.8
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Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Warm UpWarm Up
Lesson Presentation
California StandardsCalifornia Standards
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Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Warm UpWrite an algebraic expression for each word phrase.
1. a number x decreased by 9
2. 5 times the sum of p and 6
3. 2 plus the product of 8 and n
4. the quotient of 4 and a number c
x – 9
5(p + 6)
2 + 8n
4c__
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Preparation for AF4.0 Students solve simple linear equations and inequalities over the rational numbers.
Also covered: AF1.3
California Standards
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Just as with addition and subtraction equations, you can use an identity property to solve multiplication and division equations.
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
You can solve the properties of equality along with the Identity Property of Multiplication to solve multiplication and division equations.
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Solve.
6x = 48
Additional Example 1A: Solving Equations Using Division
6x = 48
1x = 8
Since x is multiplied by 6, divide both sides by 6 to undo the multiplication.
6x = 486 6
x = 8 Identity Property of Multiplication: 1 • x = x
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Solve.
–9y = 45
Additional Example 1B: Solving Equations Using Division
–9y = 45
1y = –5
–9y = 45–9 –9
y = –5 Identity Property of Multiplication: 1 • y = y
Since y is multiplied by –9, divide both sides by –9 to undo the multiplication.
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Solve.
9x = 36
Check It Out! Example 1A
9x = 36
1x = 4
9x = 369 9
x = 4 Identity Property of Multiplication: 1 • x = x
Since x is multiplied by 9, divide both sides by 9 to undo the multiplication.
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Solve.
–3y = 36
Check It Out! Example 1B
–3y = 36
1y = –12
–3y = 36–3 –3
y = –12Identity Property of Multiplication: 1 • y = y
Since y is multiplied by –3, divide both sides by –3 to undo the multiplication.
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Additional Example 2: Solving Equations Using Multiplication
Solve = 5. b–4
b–4 = 5–4 • –4 •
Since b is divided by –4, multiply both sides by –4 to undo the division.
1b = –20
Identity Property of Multiplication: 1 ● b = b
b = –20
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Solve = 5.
Check It Out! Example 2
c–3
c–3 = 5–3 • –3 •
Since c is divided by –3, multiply both sides by –3 to undo the division.
1c = –15
c = –15Identity Property of Multiplication: 1 ● c = c
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Additional Example 3: Sports Application
number of peopleTotal number of
person-hours =
• =x 450
1x = 18
It takes 450 person-hours to prepare a convention center for a conference. The director of the convention center assigns 25 people to the job. If each person works the same number of hours, how long does each person work?
Write the equation.
Since x is multiplied by 25, divide both sides by 25 to undo the multiplication.
number of hours each person works
25
25x = 450
Each person works for 18 hours.
252525x = 450
x = 18 Identity Property of Multiplication: 1 ● x = x
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Check It Out! Example 3
number of peopleTotal number of
person-hours =
• =x 320
1x = 20
It takes 320 person-hours to prepare a concert hall for a concert. The director of the concert hall assigns 16 people to the job. If each person works the same number of hours, how long does each person work?
Write the equation.
Since x is multiplied by 16, divide both sides by 16 to undo the multiplication.
number of hours each person works
16
16x = 320
Each person works for 20 hours.
161616x = 320
x = 20 Identity Property of Multiplication: 1 ● x = x
Evaluating Algebraic Expressions
1-8 Solving Equations by Multiplying or Dividing
Lesson QuizSolve.
1. 3t = 9 2. –15 = 3b
3. = –7 4. z ÷ 4 = 22
5. A roller coaster descends a hill at a rate of 80 feet per second. The bottom of the hill is 400 feet from the top. How long will it take the coaster rides to reach the bottom?
t = 3
z = 88
5 seconds
b = –5
x = 28x–4
6. A lot must be cleared so that a new building can be constructed. A crew of 7 workers is assigned to the task and each person works the same number of hours. It takes 525 person-hours to complete the job. How many hours does each person work? 75 hr