Solving Two-Step Equations

Day OneMs. Turk, Algebra 1

Unit 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!

Example 1

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 - 42x = 6

2x 2 = 6 2x = 3

2x + 4 = 10

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€

22 −2 = m4+ 2 −2

€

22 = m4+ 2

€

20 = m4

Example 3

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.

-x + 6 - 6 = -12 - 6

-x = -18-1x = -18

-1x -1 = -18 -1x = 18

-x + 6 = -12

Example 4

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.

5x + 9 = -21

5x + 9 - 9 = -21 - 95x = -30

5x 5 = -30 5

x = -6

5x + 9 = -21

Real World Problem Solving

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.

Bouquet of Flowers

Real World Problem Solving

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

Bouquet of Flowers

Real World Problem Solving

2.50r + 3.25 = 18.25 - 3.25 -3.25

2.50r = 15.002.50r 2.50 = 15.00 2.50

r = 6You can afford to buy 6 roses.

Real World Problem Solving

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.

Nice Day for a Walk

Real World Problem Solving

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

Nice Day for a Walk

Real World Problem Solving

200n + 800 = 13,000 - 800 -800

200n = 12,200200n 200 = 12,200 200

n = 61You will need to walk for 61 more minutes.

Real World Problem Solving

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.

Now you try!

Real World Problem Solving

Now you try!Relate: Cost per tulip bulb times number of bulbs plus shipping equals amount to spend.

Define: b = number of bulbs

Write: .75b + 3 = 14

Real World Problem Solving

Now you try!.75b + 3 = 14

- 3 - 3.75b = 11

.75b .75 = 14 .75b = 14.67

You can buy 14 tulip bulbs.

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!