1. Solving Two-Step Equations
Day One
Ms. Turk, Algebra 1
Unit 2-2

2. The Basics
First Step: Deal with the addition or subtraction to get the variable alone on one side of the equation.
Second Step: Multiply or divide as needed. Remember the rules for a one-step problem!

3. Example 1
2x + 4 = 10
Is there any adding or subtracting being done?
Subtract 4 from both sides.
Is there any multiplying or dividing being done?
Divide each side by 2.
2x + 4 = 10
2x =
2x = 6
2x  2 = 6  2
x = 3

4. Example 2
Is there any adding or subtracting being done to the variable?
Subtract 2 from both sides.
Is there any multiplying or dividing being done?
Multiply both sides by 4.
(4) (4)
m = 80

5. Example 3 -x + 6 = -12 x = 18 -x + 6 - 6 = -12 - 6
Is there any adding or subtracting going on?
Subtract 6 from both sides.
Is there any multiplying or dividing going on?
Divide both sides by -1.

6. Example 4
5x + 9 = -21
5x + 9 = -21
5x =
5x = -30
5x  5 = -30  5
x = -6
Is there any adding or subtracting happening?
Subtract 9 from both sides.
Is there any multiplying or dividing going on?
Divide both sides by 5.

7. Real World Problem Solving
Bouquet of Flowers
You want to buy a bouquet of baby’s breath and roses and you have $18.25 to spend. The baby’s breath is $3.25 per bunch and roses are $2.50 each. How many roses can you buy? Write and solve an algebraic equation.

8. Real World Problem Solving
Bouquet of Flowers
Relate: $2.50 times number of roses plus $3.25 equals $18.25.
Define: r = number of roses
Write: 2.50r = 18.25

9. Real World Problem Solving
2.50r = 15.00
2.50r  2.50 =  2.50
r = 6
You can afford to buy 6 roses.

10. Real World Problem Solving
Nice Day for a Walk
Suppose you walk at a rate 200 ft/min. You need to walk 13,000 feet. How many more minutes will it take you to finish if you have already walked 800 feet? Write and solve an algebraic equation.

11. Real World Problem Solving
Nice Day for a Walk
Relate: Feet per minute times number of minutes plus distance already walked equals total distance.
Define: n = number of minutes
Write: 200n = 13,000

12. Real World Problem Solving
200n = 12,200
200n  200 = 12,200  200
n = 61
You will need to walk for 61 more minutes.

13. Real World Problem Solving
Now you try!
You are ordering tulips bulbs out of a catalog. You have $14 to spend. Bulbs are $0.75 each and there is a flat shipping fee of $3. Write and solve an algebraic equation to find out how many bulbs you can buy.

14. Real World Problem Solving
Now you try!
Relate: Cost per tulip bulb times number of bulbs plus shipping equals amount to spend.
Write: .75b + 3 = 14
Define: b = number of bulbs

15. Real World Problem Solving
Now you try!
.75b + 3 = 14
.75b = 11
.75b  .75 = 14  .75
b = 14.67
You can buy 14 tulip bulbs.

16. Classwork Workbook page 22: Problems 1-8 and 12-32 even.
Write problems on notebook paper and show all steps. You’ll be turning this in!