1. Warm Up
Solve.
1. 3x = 102
= 15
3. z – 100 = 21
w = 98.6
x = 34 y 15
y = 225
z = 121
w = 19.5

2. A multi-step equation requires more than two steps to solve
A multi-step equation requires more than two steps to solve. To solve a multi-step equation, you may have to simplify the equation first by combining like terms.

3. Additional Example 1: Solving Equations That Contain Like Terms
Solve.
8x x – 2 = 37
Commutative Property of Addition
8x + 3x + 6 – 2 = 37
11x + 4 = 37 Combine like terms.
– 4 – 4 Since 4 is added to 11x, subtract 4 from both sides to undo the addition.
11x = 33 33 11
11x =
Since x is multiplied by 11, divide both sides by 11 to undo the multiplication..
x = 3

4. 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.

5. Additional Example 2A: Solving Equations That Contain Fractions
Solve.
+ = – 5n 4 7 4 3 4 7 4 –3 5n
= 4
( ) ( )
Multiply both sides by 4.
( ) ( ) ( ) 5n 4 7 –3
= 4
Distributive Property
( ) ( ) ( ) 5n 4 7 –3
= 4
Simplify.
5n + 7 = –3

6. Additional Example 2A Continued
– 7 –7 Since 7 is added to 5n, subtract from both sides to undo the addition.
5n = –10 5n 5
–10 =
Since n is multiplied by 5, divide both sides by 5 to undo the multiplication.
n = –2

7. The least common denominator (LCD) is the smallest number that each of the denominators will divide into evenly.
Remember!

8. Additional Example 2B: Solving Equations That Contain Fractions
Solve.
+ – = x 2 7x 9 17 2 3
( ) ( ) x 2 3 7x 9 17
– = 18
Multiply both sides by 18, the LCD.
18( ) + 18( ) – 18( ) = 18( ) 7x 9 x 2 17 3
Distributive Property
18( ) + 18( ) – 18( ) = 18( ) 7x 9 x 2 17 3 2 9 2 6
Simplify. 1 1 1 1
14x + 9x – 34 = 12

9. Additional Example 2B Continued
23x – 34 = Combine like terms.
Since 34 is subtracted from x, add 34 to both sides.
23x = 46 =
23x 23 46
Since x is multiplied by 23, divide t both sides by 23.
x = 2

10. 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 the two days is 12 mi/h, how far did he ride on Monday? Round your answer to the nearest tenth of a mile.
David’s average speed is his total distance for the two days divided by the total time.
Total distance
Total time =
average speed

11. Additional Example 3 Continued
2 + 5
= 12
m + 3m
Substitute m + 3m for total distance and for total time. 7
= 12 4m
Simplify.
= 7(12) 7 4m
Multiply both sides by 7.
4m = 84
84 4
4m 4 =
Divide both sides by 4.
m = 21
David rode 21 miles on Monday.

12. Lesson Review! Solve. 1. 6x + 3x – x + 9 = 33 2. 29 = 5x + 21 + 3x=
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?
x = 3
x = 1 5 8 x 8 33 8
x = 28
x = 1 9 16
– = 6x 7 2x 21 25 21
$8.50