1. Solving Two-Step Equations

2. 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.

3. 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

4. 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

5. 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

6. 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

7. Try These Examples 1.2x – 5 = 17 2.3y + 7 = 25 3.5n – 2 = 38 x = 11 y = 6 n = 8

8. Ex. 5: Solve x + 4 = 9 3 x 3 + 4 = 9 - 4 (Subtract 4 from both sides) x 3 = 5 x 3 = 5 3 3 (Mult. by 3 on both sides) x = 15

9. Ex. 6: Solve r + 1 = 6 4 r 4 + 1 = 6 - 1 (Subtract 1 from both sides) r 4 = 5 r 4 = 5 4 4 (Mult. by 4 on both sides) r = 20

10. Ex. 7: Solve m + 1 = -10 -11 M -11 + 1 = -10 - 1 (Subtract 1 from both sides) m -11 = -11 m -11 = -11 -11 -11 (Mult. by -11 on both sides) m = 121

11. Try these examples! 1.x – 3 = 8 5 2. c + 4 = 9 7 3. r – 6 = 2 3 x = 55 c = 35 r = 24

12. 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?

13. Equations and Word Problems 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?

14. Equations and Word Problems 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?

15. Equations and Word Problems 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?

16. Equations and Word Problems 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?

17. Equations and Word Problems 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?