This document provides instruction on solving multi-step equations. It begins with warm-up problems, then presents a problem of the day involving a word problem with three unknown amounts of money. The lesson explains how to solve multi-step equations by combining like terms and isolating the variable. It provides examples involving integers, fractions, and a travel word problem. The document concludes with a check it out section providing additional practice problems and a lesson quiz.

1. 11-2 Solving Multi-Step Equations
11-2 Solving Multi-Step Equations
Warm Up
Problem of the Day
Lesson Presentation
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2. 11-2 Solving Multi-Step Equations
Warm Up
Solve.
1. 3x = 102 x = 34
y
2. 15 = 15 y = 225
3. z – 100 = 21 z = 121
4. 1.1 + 5w = 98.6 w = 19.5
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3. 11-2 Solving Multi-Step 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
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4. 11-2 Solving Multi-Step Equations
Learn to solve multi-step equations.
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5. 11-2 Solving Multi-Step Equations
To solve a multi-step equation, you
may have to simplify the equation first
by combining like terms.
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6. 11-2 Solving Multi-Step Equations
Additional Example 1: Solving Equations That
Contain Like Terms
Solve.
8x + 6 + 3x – 2 = 37
11x + 4 = 37 Combine like terms.
– 4 – 4 Subtract 4 from both sides.
11x = 33
11x = 33
11 11 Divide both sides by 11.
x=3
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7. 11-2 Solving Multi-Step Equations
Additional Example 1 Continued
Check
8x + 6 + 3x – 2 = 37
?
8(3) + 6 + 3(3) – 2 = 37 Substitute 3 for x.
?
24 + 6 + 9 – 2 = 37
?
37 = 37 
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8. 11-2 Solving Multi-Step Equations
Check It Out: Example 1
Solve.
9x + 5 + 4x – 2 = 42
13x + 3 = 42 Combine like terms.
– 3 – 3 Subtract 3 from both sides.
13x = 39
13x = 39 Divide both sides by 13.
13 13
x=3
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9. 11-2 Solving Multi-Step Equations
Check It Out: Example 1 Continued
Check
9x + 5 + 4x – 2 = 42
?
9(3) + 5 + 4(3) – 2 = 42 Substitute 3 for x.
?
27 + 5 + 12 – 2 = 42
?
42 = 42 
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10. 11-2 Solving Multi-Step 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.
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11. 11-2 Solving Multi-Step Equations
Additional Example 2A: Solving Equations That
Contain Fractions
Solve.
5n+ 7= – 3
4 4 4
Multiply both sides by 4 to clear fractions,
and then solve.
( ) ( )
4 5n + 7 = 4 4
4 4
–3
4( 4)+ 4(7 )= 4( 4) Distributive Property.
5n –3
4
5n + 7 = –3
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12. 11-2 Solving Multi-Step Equations
Additional Example 2A Continued
5n + 7 = –3
– 7 –7 Subtract 7 from both sides.
5n = –10
5n= –10 Divide both sides by 5
5 5
n = –2
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13. 11-2 Solving Multi-Step Equations
Remember!
The least common denominator (LCD) is the
smallest number that each of the denominators
will divide into.
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14. 11-2 Solving Multi-Step Equations
Additional Example 2B: Solving Equations That
Contain Fractions
Solve.
7x + x – 17 = 2
9 2 9 3
The LCD is 18.
( ) ()
17 Multiply both
18 7x + x – 9 = 18 2 sides by 18.
9 2 3
18( 9) + 18(2 ) – 18(9 ) = 18( 3)Property.
7x x 17 2 Distributive
14x + 9x – 34 = 12
23x – 34 = 12 Combine like terms.
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15. 11-2 Solving Multi-Step Equations
Additional Example 2B Continued
23x – 34 = 12 Combine like terms.
+ 34 + 34 Add 34 to both sides.
23x = 46
23x = 46 Divide both sides by 23.
23 23
x=2
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16. 11-2 Solving Multi-Step Equations
Additional Example 2B Continued
Check
7x + x – 17 = 2
9 2 9 3
7(2) (2) 17 ? 2
9 + 2 – 9 =3 Substitute 2 for x.
14 + 2 – 17 = 2
?
9 2 9 3
14 + – 17 = 2?
1
9 9 3
14 + 9 – 17 = 6
?
9 9 9 9 The LCD is 9.
6= 6
?
9 9
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17. 11-2 Solving Multi-Step Equations
Check It Out: Example 2A
Solve.
3n+ 5= – 1
4 4 4
Multiply both sides by 4 to clear fractions,
and then solve.
( ) ( )
4 3n + 5 = 4 4
4 4
–1
4( 4)+ 4(5 )= 4( 4)
3n –1
4 Distributive Property.
3n + 5 = –1
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18. 11-2 Solving Multi-Step Equations
Check It Out: Example 2A Continued
3n + 5 = –1
– 5 –5 Subtract 5 from both sides.
3n = –6
3n= –6 Divide both sides by 3.
3 3
n = –2
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19. 11-2 Solving Multi-Step Equations
Check It Out: Example 2B
Solve.
5x + x – 13 = 1
9 3 9 3
The LCD is 9.
( ) () 13 1 Multiply both
9 5x +x – 9 =9 3 sides by 9.
9 3
( ) ( ) ( ) = 9(3 )
5x x
9 9 +9 3 –9 9
13
1 Distributive
Property.
5x + 3x – 13 = 3
8x – 13 = 3 Combine like terms.
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20. 11-2 Solving Multi-Step Equations
Check It Out: Example 2B Continued
8x – 13 = 3 Combine like terms.
+ 13 + 13 Add 13 to both sides.
8x = 16
8x = 16
8 8 Divide both sides by 8.
x=2
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21. 11-2 Solving Multi-Step Equations
Check It Out: Example 2B Continued
Check
5x + x – 13 = 1
9 3 9 3
5(2) (2) 13 ? 1
9 + 3 – 9 =3 Substitute 2 for x.
10 + 2 – 13 = 1
?
9 3 9 3
10 + 6 – 13 = 3
?
9 9 9 9 The LCD is 9.
3= 3
?
9 9
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22. 11-2 Solving Multi-Step Equations
Additional Example 3: Travel Application
On Monday, David rides his bicycle m miles in
2 hours. On Tuesday, he rides three times as
far in 5 hours. If his average speed for two
days is 12 mi/h, how far did he ride on the
second day? Round your answer to the nearest
tenth of a mile.
David’s average speed is his combined speeds for
the two days divided by 2.
Day 1 speed + Day 2 speed = average speed
2
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23. 11-2 Solving Multi-Step Equations
Additional Example 3 Continued
m + 3m m
Substitute 2 for Day 1 speed
2 5
= 12 3m
2 and for Day 2 speed.
5
m 3m
+
1 2 5 Multiply both sides by 2.
2 = 2(12)
21
m + 3m Multiply both sides by the
10 = 10(24)
2 5 LCD 10.
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24. 11-2 Solving Multi-Step Equations
Additional Example 3 Continued
5m + 6m = 240 Simplify.
11m = 240 Combine like terms. Divide
11 11 both sides by 11.
m ≈ 21.82
On the second day David rode 3 times m (3m)
or approximately 65.5 miles.
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25. 11-2 Solving Multi-Step Equations
Check It Out: Example 3
On Saturday, Penelope rode her scooter m
miles in 3 hours. On Sunday, she rides twice
as far in 7 hours. If her average speed for two
days is 20 mi/h, how far did she ride on
Sunday? Round your answer to the nearest
tenth of a mile.
Penelope’s average speed is her combined speeds
for the two days divided by 2.
Day 1 speed + Day 2 speed = average speed
2
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26. 11-2 Solving Multi-Step Equations
Check It Out: Example 3 Continued
m + 2m m
Substitute 3 for Day 1 speed
3 7
= 20 2m
2 and for Day 2 speed.
7
m 2m
+
1 3 7 Multiply both sides by 2.
2 = 2(20)
21
m + 2m Multiply both sides by the
21 = 21(40)
3 7 LCD 21.
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27. 11-2 Solving Multi-Step Equations
Check It Out: Example 3 Continued
7m + 6m = 840 Simplify.
13m = 840 Combine like terms. Divide
13 13 both sides by 13.
m ≈ 64.62
On Sunday Penelope rode 2 times m, (2m), or
approximately 129.2 miles.
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28. 11-2 Solving Multi-Step Equations
Lesson Quiz
Solve.
1. 6x + 3x – x + 9 = 33 x=3
2. –9 = 5x + 21 + 3x x = –3.75
3. 5 + x = 33 x = 28
8 8 8
9
4. 6x – 2x = 25 x = 116
7 21 21
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? $8.50
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