Solving Two-Step Equations

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 4 - 4 10 - 4
• 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 6 - 6 -12 - 6
• -x -18
• -1x -18
• -1x ? -1 -18 ? -1
• x 18

• 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 9 - 9 -21 - 9
• 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 babys breath and
  roses and you have 18.25 to spend. The babys
  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 3.25 18.25

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Real World Problem Solving

• 2.50r 3.25 18.25
• - 3.25 -3.25
• 2.50r 15.00
• 2.50r ? 2.50 15.00 ? 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 800 13,000

12
Real World Problem Solving

• 200n 800 13,000
• - 800 -800
• 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
- 3 - 3
.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. Youll be turning this in!