2-2 Solving Equations by 2-2 Multiplying or...
Transcript of 2-2 Solving Equations by 2-2 Multiplying or...
2-2Solving Equations by Multiplying or Dividing2-2Solving Equations by Multiplying or Dividing
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Holt Algebra 1Holt Algebra 1
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Lesson QuizLesson Quiz
2-2Solving Equations by Multiplying or Dividing
Bell Quiz 2-2
Solve each equation. Check your answer.
1. u -15 = -8
2. 19 + a = 19
3 pts
3 pts
Holt Algebra 1
2. 19 + a = 19
3. -12 + f = 3
10 pts
possible
3 pts
3 pts
1 pt for putting your name on
your quiz ☺☺☺☺
2-2Solving Equations by Multiplying or Dividing
Questions on 2-1
Holt Algebra 1
2-2Solving Equations by Multiplying or Dividing
Solve one-step equations in one variable by
using multiplication or division.
Objective
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2-2Solving Equations by Multiplying or Dividing
Inverse Operations
Solving an equation that contains multiplication or division is similar to solving an equation that contains addition or subtraction. Use inverse operations to undo the operations on the variable.
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Inverse Operations
Operation Inverse Operation
Multiplication Division
Division Multiplication
2-2Solving Equations by Multiplying or Dividing
Solve the equation.
Example 1A: Solving Equations by Using
Multiplication
Since j is divided by 3,
multiply both sides by 3
–8 =j
3
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multiply both sides by 3
to undo the division.
To check your solution,
substitute –24 for j in the
original equation.
Check –8 =j
3
2-2Solving Equations by Multiplying or Dividing
Solve the equation.
Example 1B: Solving Equations by Using
Multiplication
Since n is divided by 6,
multiply both sides by 6
= 2.8n
6
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multiply both sides by 6
to undo the division.
To check your solution,
substitute 16.8 for n in the
original equation.
Check = 2.8n
6
2-2Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 1
1a: = 10p
5
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1b: –13 =y
3
1c: = 7c
8
2-2Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Example 2A: Solving Equations by Using Division
Since y is multiplied by 9,
divide both sides by 9 to
9y = 108
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divide both sides by 9 to
undo the multiplication.
To check your solution,
substitute 12 for y in the
original equation.
Check 9y = 108
2-2Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Example 2B: Solving Equations by Using Division
Since v is multiplied by –6,
divide both sides by –6 to
–4.8 = –6v
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undo the multiplication.
To check your solution,
substitute 0.8 for v in the
original equation.
Check –4.8 = –6v
2-2Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 2
2a: 16 = 4c
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2b: 0.5y = –10
2c: 15k = 75
2-2Solving Equations by Multiplying or Dividing
Remember that dividing is the same as multiplying by the reciprocal. When solving equations, you will sometimes find it easier to multiply by a reciprocal
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find it easier to multiply by a reciprocal instead of dividing. This is often true when an equation contains fractions.
2-2Solving Equations by Multiplying or Dividing
Solve the equation.
Example 3A: Solving Equations That Contain
Fractions
w = −−−−2056 The reciprocal of is . Since w is
multiplied by , multiply both sides
56
65
56
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To check your solution,
substitute −24 for w in the
original equation.
Check w = −205
6
multiplied by , multiply both sides
by .6
65
2-2Solving Equations by Multiplying or Dividing
Solve the equation.
Example 3B: Solving Equations That Contain
Fractions
= z316
18 The reciprocal of is 8. Since z is
multiplied by , multiply both sides
18
18
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To check your solution,
substitute for z in the
original equation.
32
multiplied by , multiply both sides
by 8.
18
Check1
8
316
= z
2-2Solving Equations by Multiplying or Dividing
Solve the equation. Check your answer.
Check It Out! Example 3a
3a: – = b14
15
4j 2
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3b: =4j6
23
13c: w = 102
6
2-2Solving Equations by Multiplying or Dividing
Example 4: Application
Ciro puts of the money he earns from mowing lawns into a college education fund. This year Ciro added $285 to his college education fund. Write and solve an equation to find how much money Ciro earned mowing lawns this year.
14
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Write an equation to represent the relationship.
one-fourth times earnings equals college fund
Substitute 285 for c. Since m is divided
by 4, multiply both sides by 4 to undo
the division.
Ciro earned $1140 mowing lawns.
2-2Solving Equations by Multiplying or Dividing
WORDS
Addition Property of Equality
You can add the same number to both sides of an equation, and the statement will still be true.
3 = 3
Properties of Equality
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NUMBERS
3 = 3
3 + 2 = 3 + 2
5 = 5
ALGEBRAa = b
a + c = b + c
2-2Solving Equations by Multiplying or Dividing
WORDS
Subtraction Property of Equality
You can subtract the same number from both sides of an equation, and the statement will still be true.
7 = 7
Properties of Equality
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NUMBERS
7 = 7
7 – 5 = 7 – 5
2 = 2
ALGEBRAa = b
a – c = b – c
2-2Solving Equations by Multiplying or Dividing
WORDS
Multiplication Property of Equality
You can multiply both sides of an equation by the same number, and the statement will still be true.
6 = 6
Properties of Equality
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NUMBERS
6 = 6
6(3) = 6(3)
18 = 18
ALGEBRAa = b
ac = bc
2-2Solving Equations by Multiplying or Dividing
Properties of EqualityDivision Property of Equality
You can divide both sides of an equation by the same nonzero number, and the statement will still be true.
WORDS
8 = 8
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a = b(c ≠ 0)
8 = 8
2 = 2
ALGEBRA
NUMBERS 8
4
8
4=
ac
ac
=
2-2Solving Equations by Multiplying or Dividing
HOMEWORKSec 2-2: (Pg 87) 1, 4, 7, 10, 13, 16, 20, 21-44 all, 52, 57, 96, 104
Holt Algebra 1
52, 57, 96, 104