Solving Two-Step Equations. When solving algebraic equations our main goal is to get the variable...

Solving Two-Step Equations

When solving algebraic equations our main goal is to get the variable (letter) by itself.

Step One: use inverse operations to move the number that is NOT

attached to the letter.

Step Two: use inverse operations to move the number that IS attached to the letter.

Ex. 1: Solve 4x – 5 = 15

4x – 5 = 15 +5 +5 (Add 5 to both sides)

4x = 20 4 4 (Divide both sides by

4)

x = 5

Ex. 2: Solve 5n – 18 = -33

5n – 18 = -33 + 18 +18 (Add 18 to both sides)

5n = -15 5 5 (Divide both sides by 5)

n = -3

Ex. 3: Solve 5h + 3 = 18

5h + 3 = 18 - 3 - 3 (Subtract 3 from both sides)

5h = 15 5 5 (Divide both sides by 5)

h = 3

Ex. 4: Solve 4m + 12 = 52

4m + 12 = 52 - 12 -12 (Subtract 12 from both

sides)

4m = 40 4 4 (Divide both sides by 4)

m = 10

Try These Examples

1. 2x – 5 = 17

2. 3y + 7 = 25

3. 5n – 2 = 38

x = 11

y = 6

n = 8

Ex. 5: Solve x + 4 = 9 3x

3+ 4 = 9- 4 - 4 (Subtract 4 from both sides)

x 3

= 5

x 3

= 5 • 3 • 3 (Mult. by 3 on both sides)

x = 15

Ex. 6: Solve r + 1 = 6 4r

4+ 1 = 6- 1 - 1 (Subtract 1 from both sides)

r 4

= 5

r 4

= 5 • 4 • 4 (Mult. by 4 on both sides)

r = 20

Ex. 7: Solve m + 1 = -10 -11 M

-11+ 1 = -10- 1 - 1 (Subtract 1 from both sides)

m -11

= -11

m -

11

= -11 • -11 • -11 (Mult. by -11 on both sides)

m = 121

Try these examples!

1. x – 3 = 8 5

2. c + 4 = 9 7

3. r – 6 = 2 3

x = 55

c = 35

r = 24

Equations and Word Problems

Jennifer has $22.75 in her bank. She saves quarters and half dollars. She has $10.50in half dollars. How many quarters does she have?


On a trip, a family drove an average of 250 miles each day. If the family drove a total of 3,000 miles on their trip, how many days were they gone?


A jacket costs $28 more than twice the cost of a pair of slacks. If the jacket costs $152, how much so the slacks cost?


The monthly fee for cable is $25 plus $4.50 per movie channel. Tamara paid $56.50 in May for her cable bill. How many movie channels did he get?


A garage charged $248 in parts and $30 per hour in labor for working on a car. How many hours did the garage spend working on the car if the total bill was $572?


The monthly fee for cable is $25 plus $4.50 per movie channel. Tamara paid $56.50 in May for her cable bill. How many movie channels did he get?

Solving Two-Step Equations. When solving algebraic equations our main goal is to get the variable...

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