Solving and Graphing Linear Inequalities

Single Variable Inequalities

100

x - 7 > 16

x > 23

200

-4x < 24

x > -6

300

2x + 8 > -12

x > 10

400

-5(3 - x) + 21 < -3x + 14

x < 1

500

You want to spend no more than 80 dollars on an outfit for you birthday party. You have already spend 56 dollars on a shirt. Write an inequality to represent the possible cost of the rest of your outfit.

80 > 56 + x (greater than or equal to)

Compound Inequalities

100

-6 < 3x - 7 < 5

1/3 < x < 4

200

4 < 1/2x + 2 < 8

4 < x < 12

300

7x - 9 > 12 or -3x + 1 > 7

x > 3 or x < -2

400

6x + 10 < 8 or 4x - 3 > 9

x < -1/3 or x > 3

500

Translate: Five more than x is less than 8 or 3 less than x is greater than 5

5 + x < 8 or x - 3 > 5

Absolute ValueEquations

100

|x| = 3

x = -3 or x = 3

200

|x + 6| = 5

x = -11 or x = -1

300

|6x + 1| = -4

no solution

400

3|2x - 2| + 4 = 10

x = 2 or x = 0

500

The minimum and maximum values of 25 with an absolute deviation of 0.55.

24.45 and 25.55

Absolute Value Inequalities

100

|x| > 12

x > 12 or x < -12

200

|x| < 3

-3 < x < 3

300

|4x - 3| < 5

-1/2 < x < 2

400

2|5x + 1| > 22

x > 2 or x < -2 2/5

500

4|x - 9| - 5 < 11

5 < x < 13

Graphing

100

Is (-2, 3) a solution to 2x - y > -9?

YES; -7 > -9

200

Graph: y > -x + 8

See Whiteboard

300

Graph: y < 2/3 x - 4

See Whiteboard

400

Graph: x > -2

See Whiteboard

500

Graph: 2x - 3y < 6

See Whiteboard