1. Lesson 2 Solving Inequalities
Using Multiplication and Division

2. Bell Ringer Solve the following equations.
3x = 9
z/4 = 3
4y = 16
(1/2)m = 4
(click for answers)
If you got:
x = 3
z = 12
y = 4
m = 8
GREAT JOB!

3. Show me how you got the bell ringer.
3x = 9 (undo the multiplication with division)
3/3 x = 9/3 (simplify both sides)
x = 3
You can check your answer by substituting the value of x into the original equation.
3(3) = 9 : this is a true statement, therefore x = 3 is correct!
= 3 (undo the division with multiplication)
4( )= 3(4)
Z = 12
4y = 16
4/4y = 16/4 (divide both sides by 4)
y = 4
4. (1/2)m = 4 (mult. by the inverse of (1/2)
(2/1)(1/2)m = 4(2/1)
m = 8

4. Multiplying by a Positive Number
If each side of a true inequality is multiplied by the same Positive number, the resulting inequality is also true.
Algebraically: If a and b are any numbers and c is a positive number, the following are true.
If a > b, then ac > bc, and if a < b, then ac < bc
Example: 6 > 5, then 6(3) > 5(3)
18 > 15

5. Multiplying by a Negative Number
If each side of a true inequality is multiplied by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.
Algebraically: If a and b are any numbers and c is a negative number, the following are true.
If a > b, then ac < bc, and if a < b, then ac > bc.
Example: 5 > 4, then 5(-2) < 4(-2)
-10 < -8 √

6. Dividing by a Positive Number
If each side of a true inequality is divided by the same Positive number, the resulting inequality is also true.
Algebraically: If a and b are any numbers and c is a positive number, the following are true.
If a > b, then a/c > b/c, and if a < b, then a/c < b/c
Example: 9 > 6, then 9/(3) > 6/(3)
3 > 2

7. Dividing by a Negative Number
If each side of a true inequality is divided by the same negative number, the direction of the inequality symbol must be reversed so that the resulting inequality is also true.
Algebraically: If a and b are any numbers and c is a negative number, the following are true.
If a > b, then a/c < b/c, and if a < b, then a/c > b/c.
Example: 6 > 4, then 6/(-2) < 4/(-2)
-3 < -2 √

8. Here’s Some Problems 6g < 144 -14d > 84 -(3/4)q < -33
Five times a number is less than or equal to ten.
Hint: 5n < 10
If you got:
g < 24
d < -6
q > 44
n < 2