1. Multiplying or Dividing 2-2
Solving Equations by
Multiplying or Dividing
2-2
Hand in HW – p 80 to front table
2-2 Notes, HW p 87
# 21-44,
Holt Algebra 1

2. Objective
I will:
Solve one-step equations in one variable by using multiplication or division.

3. Solving Equations Using Multiplication
2-2
Solving Equations by Multiplying or Dividing
Course 3
Solving Equations Using Multiplication
Think…. What type of problem is this and how do I “undo” it? b –4
Solve = 5. b –4
= 5
–4 •
• –4
Multiply both sides by –4.
b = –20
Check b –4
= 5
–20 –4
= 5 ?
Substitute –20 for b.
5 = 5 ? 

4. 2-2 Solving Equations by Multiplying or Dividing
Course 3
Check It Out: Example 2 c –3
Solve = 5. c –3
= 5
–3 •
• –3
Multiply both sides by –3.
c = –15
Check c –3
= 5
–15 –3
= 5 ?
Substitute –15 for c.
5 = 5 ? 

5. Example 2A: Solving Equations by Using Division
Solve the equation. Check your answer.
9y = 108
Since y is multiplied by 9, divide both sides by 9 to undo the multiplication.
y = 12
Check 9y = 108
To check your solution, substitute 12 for y in the original equation.
9(12) 108 

6. Example 2B: Solving Equations by Using Division
Solve the equation. Check your answer.
–4.8 = –6v
Since v is multiplied by –6, divide both sides by –6 to undo the multiplication.
0.8 = v
Check –4.8 = –6v
–4.8 –6(0.8)
To check your solution, substitute 0.8 for v in the original equation.
–4.8 –4.8 

7. Check It Out! Example 2a
Solve the equation. Check your answer.
16 = 4c
Since c is multiplied by 4, divide both sides by 4 to undo the multiplication.
4 = c
Check = 4c
16 4(4)
To check your solution, substitute 4 for c in the original equation. 

8. Check It Out! Example 2c
Solve the equation. Check your answer.
15k = 75
Since k is multiplied by 15, divide both sides by 15 to undo the multiplication.
k = 5
Check 15k = 75
To check your solution, substitute 5 for k in the original equation.
15(5) 75 

9. Remember that dividing is the same as multiplying by the reciprocal.
Instead of dividing by a fraction to get the variable alone, you multiply both sides by the reciprocal.

10. What is the reciprocal of:
5/6 2
-9/8

11. Example 3A: Solving Equations That Contain Fractions
Solve the equation. 5
w = 20 6
The reciprocal of is Since w is multiplied by , multiply both sides by 5 6
w = 24
Check
w = 20 5 6
To check your solution, substitute 24 for w in the original equation.
20
20 20 

12. Example 3B: Solving Equations That Contain Fractions
Solve the equation. 3 1 8
= z 16
The reciprocal of is 8. Since z is multiplied by , multiply both sides by 8. 1 8
= z 3 2
Check 1 8 3 16
= z
To check your solution, substitute for z in the original equation. 3 2 3 16 

13. Solve the equation. Check your answer. 1 4 1 5 – = b
Check It Out! Example 3a
Solve the equation. Check your answer. 1 4 1 5
– = b
The reciprocal of is 5. Since b is multiplied by , multiply both sides by 5. 1 5
= b 5 4 –
= b 5 4
Check 1 –
To check your solution, substitute – for b in the original equation. 5 4 