1. Inequalities with Variables on the Right Side

2. Inequalities and their Graphs
3 < x
<
3 is less than x
x is greater than 3
x 3 -1 1 2 3 4 5

3. Inequalities and their Graphs
-2 > x
>
-2 is greater than x
x is less than -2
x -2 -5 -4 -3 -2 -1 1

4. - 1 -1 Solving an inequality 3 > x + 1 2 > x > x 2
2 > x
>
x 2
Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3
Choose x = 0, is 3 > x + 1 true?
3 > 0 + 1
3 > 1 

5. - 1 -1 Solving an inequality > OR 3 > x + 1 x + 1 3 x < 2
x < 2
Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3
Choose x = 0, is 3 > x + 1 true?
3 > 0 + 1
3 > 1 

6. +2 +2 Solving an inequality -1 < x - 2 1 < x < x 1
1 < x
<
x 1
Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3
Choose x = 2, is 3 > x + 1 true?
-1 < 2 - 2
-1 < 0 

7. Solving an inequality 8 < 4x 4 4 2 < x < x 2 8 < 4(3)
2 < x
<
x 2
Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3
Choose x = 3, is 8 < 4x true?
8 < 4(3)
8 < 12 

8. Solving an inequality 4 < -2x < -2x 4 > -2 -2 x -2
we divided by a negative so we need to switch the sign again…..
x -2
Check: Choose a point included on the graph and see if its true….. -3 -2 -1 1 2 3
Choose x = -3, is 4 < -2x true?
4 < -2(-3)
4 < 6 