Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson...
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Transcript of Page 500 #15-32 ANSWERS. Pre-Algebra 10-2 Solving Multistep Equations Student Progress Chart Lesson...
Page 500 #15-32 ANSWERS
Pre-Algebra
10-2 Solving Multistep Equations
Student Progress Chart
Lesson Reflection
Pre-Algebra
10-2 Solving Multistep Equations
Today’s Learning Goal Assignment
Learn to solve multistep equations.
Pre-Algebra
10-2 Solving Multistep Equations
Pre-Algebra HW
Page 504#12-24
Pre-Algebra
10-2 Solving Multistep Equations10-2 Solving Multistep Equations
Pre-Algebra
Warm UpWarm Up
Problem of the DayProblem of the Day
Lesson PresentationLesson Presentation
Pre-Algebra
10-2 Solving Multistep Equations
Warm UpSolve.
1. 3x = 102
2. = 15
3. z – 100 = –1
4. 1.1 + 5w = 98.6
x = 34
y = 225
z = 99
Pre-Algebra
10-2 Solving Multistep Equations
w = 19.5
y15
Pre-Algebra
10-2 Solving Multistep Equations
Problem of the Day
Ana has twice as much money as Ben, and Ben has three times as much as Clio. Together they have $160. How much does each person have?Ana, $96; Ben, $48; Clio, $16
Pre-Algebra
10-2 Solving Multistep Equations
Today’s Learning Goal Assignment
Learn to solve multistep equations.
Pre-Algebra
10-2 Solving Multistep Equations
To solve a complicated equation, you may have to simplify the equation first by combining like terms.
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
8x + 6 + 3x – 2 = 37
Additional Example 1: Solving Equations That Contain Like Terms
11x + 4 = 37 Combine like terms.
– 4 – 4 Subtract to undo addition.11x = 33
x = 3
Divide to undo multiplication.3311
11x11
=
Pre-Algebra
10-2 Solving Multistep Equations
Check
Additional Example 1 Continued
8x + 6 + 3x – 2 = 37
8(3) + 6 + 3(3) – 2 = 37?
24 + 6 + 9 – 2 = 37?
37 = 37?
Substitute 3 for x.
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
9x + 5 + 4x – 2 = 42
Try This: Example 1
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract to undo addition.13x = 39
x = 3
Divide to undo multiplication.3913
13x13
=
Pre-Algebra
10-2 Solving Multistep Equations
Check
Try This: Example 1 Continued
9x + 5 + 4x – 2 = 42
9(3) + 5 + 4(3) – 2 = 42?
27 + 5 + 12 – 2 = 42 ?
42 = 42?
Substitute 3 for x.
Pre-Algebra
10-2 Solving Multistep Equations
If an equation contains fractions, it may help to multiply both sides of the equation by the least common denominator (LCD) to clear the fractions before you isolate the variable.
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
A. + = –
Additional Example 2: Solving Equations That Contain Fractions
34
74
5n4
Multiply both sides by 4 to clear fractions, and then solve.
( ) ( )74
–3 4
5n4
4 + = 4
( ) ( ) ( )5n4
74
–3 44 + 4 = 4
5n + 7 = –3
Distributive Property.
Pre-Algebra
10-2 Solving Multistep Equations
Additional Example 2 Continued
5n + 7 = –3 – 7 –7 Subtract to undo addition.
5n = –10
5n5
–10 5
= Divide to undo multiplication.
n = –2
Pre-Algebra
10-2 Solving Multistep Equations
The least common denominator (LCD) is the smallest number that each of the denominators will divide into.
Remember!
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
B. + – =
Additional Example 2B: Solving Equations That Contain Fractions
23
The LCD is 18.
x 2
7x9
17 9
18( ) + 18( ) – 18( ) = 18( )7x9
x2
17 9
23
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.
( )x2
23
7x9
17 918 + – = 18
Distributive Property.
Multiply both sides by the LCD.
Pre-Algebra
10-2 Solving Multistep Equations
Additional Example 2B Continued
23x = 46
= 23x23
4623 Divide to undo multiplication.
x = 2
+ 34 + 34 Add to undo subtraction.
23x – 34 = 12 Combine like terms.
Pre-Algebra
10-2 Solving Multistep Equations
Additional Example 2B Continued
69
69=
?
Check
x 2
7x9
17 9
+ – = 23
23 Substitute 2 for x.7(2)
9 + – =(2) 2
17 9
?
23
149 + – =2
2 17 9
?
23
149 + – =
17 9
?1
The LCD is 9.69
149 + – =9
9 17 9
?
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
A. + = –
Try This: Example 2A
14
54
3n4
Multiply both sides by 4 to clear fractions, and then solve.
( ) ( )54
–1 4
3n4
4 + = 4
( ) ( ) ( )3n4
54
–1 44 + 4 = 4
3n + 5 = –1
Distributive Property.
Pre-Algebra
10-2 Solving Multistep Equations
Try This: Example 2A Continued
3n + 5 = –1 – 5 –5 Subtract to undo addition.
3n = –6
3n3
–6 3
= Divide to undo multiplication.
n = –2
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
B. + – =
Try This: Example 2B
13
The LCD is 9.
x 3
5x9
13 9
9( ) + 9( )– 9( ) = 9( )5x9
x3
13 9
13
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.
( )x3
13
5x9
13 9 9 + – = 9( )
Distributive Property.
Multiply both sides by the LCD.
Pre-Algebra
10-2 Solving Multistep Equations
8x = 16
= 8x8
16 8 Divide to undo multiplication.
x = 2
+ 13 + 13 Add to undo subtraction.
8x – 13 = 3 Combine like terms.
Try This: Example 2B Continued
Pre-Algebra
10-2 Solving Multistep Equations
39
39=
?
Check
x 3
5x9
13 9
+ – = 13
13 Substitute 2 for x.5(2)
9 + – =(2) 3
13 9
?
13
109 + – =2
3 13 9
?
The LCD is 9.39
109 + – =6
9 13 9
?
Try This: Example 2B Continued
Pre-Algebra
10-2 Solving Multistep Equations
When Mr. and Mrs. Harris left for the mall, Mrs. Harris had twice as much money as Mr. Harris had. While shopping, Mrs. Harris spent $54 and Mr. Harris spent $26. When they arrived home, they had a total of $46. How much did Mr. Harris have when he left home?
Additional Example 3: Money Application
Let h represent the amount of money that Mr. Harris had when he left home. So Mrs. Harris had 2h when she left home.
h + 2h – 26 – 54 = 46Mr. Harris $+ Mrs. Harris $ – Mr. Harris spent – Mrs. Harris spent = amount left
Pre-Algebra
10-2 Solving Multistep Equations
Additional Example 3 Continued
3h – 80 = 46 Combine like terms.
+ 80 +80 Add 80 to both sides.
3h = 126
3h3
1263= Divide both sides by 3.
h = 42
Mr. Harris had $42 when he left home.
Pre-Algebra
10-2 Solving Multistep Equations
When Mr. and Mrs. Wesner left for the store, Mrs. Wesner had three times as much money as Mr. Wesner had. While shopping, Mr. Wesner spent $50 and Mrs. Wesner spent $25. When they arrived home, they had a total of $25. How much did Mr. Wesner have when he left home?
Try This: Example 3
Let h represent the amount of money that Mr. Wesner had when he left home. So Mrs. Wesner had 3h when she left home.
h + 3h – 50 – 25 = 25Mr. Wesner $ + Mrs. Wesner $ – Mr. Wesner spent – Mrs. Wesner spent = amount left
Pre-Algebra
10-2 Solving Multistep Equations
Try This: Example 3 Continued
4h – 75 = 25 Combine like terms.
+ 75 +75 Add 75 to both sides.
4h = 100
4h4
1004= Divide both sides by 4.
h = 25
Mr. Wesner had $25 when he left home.
Pre-Algebra
10-2 Solving Multistep Equations
Solve.
1. 6x + 3x – x + 9 = 33
2. –9 = 5x + 21 + 3x
3. + =
5. Linda is paid double her normal hourly rate for each hour she works over 40 hours in a week. Last week she worked 52 hours and earned $544. What is her hourly rate?
Lesson Quiz
x = –3.75
x = 3
x = 2858
x8
33 8
6x 7
4. – =2x21
2521
$8.50
x = 1 916