Solving and Graphing Linear Inequalities

One Step Inequalities

100

Solve:

x + 4 < 5

x < 1

200

Solve:

8.2 + v > -7.6

v > - 15.8

300

Solve:

2.1 > c - 6.7

c < 8.8

400

Solve:

1.02  <  -3 x

x <  - 0.34

500

Solve:

-40 < - 5r

r < 8

Multi-Step Inequalities

100

Solve: (may be no solution or all real numbers)

2x -3 > 7

x > 5

200

Solve: (may be no solution or all real numbers)

5y + 9 < 4

y < -1

300

Solve: (may be no solution or all real numbers)

-10p > 6p - 8

p < 1/2

400

Solve: (may be no solution or all real numbers)

5 ( b + 9 ) < 5b + 45

All Real Numbers

500

Solve: (may be no solution or all real numbers)

5d - 8d - 4 <  - 4 + 3d

d > 0

Compound Inequalities

100

Write the equivalent inequality:

All real numbers that are less than 6 AND greater than 2.

(triple points for correct graph)

2 < x < 6

200

Write the equivalent inequality:

All real numbers that are less than or equal to -8 OR greater than 12.

(triple points for correct graph)

x < - 8 OR x > 12

300

Graph:

6 < x + 5 < 11

open at 1, closed at 6

400

Solve:

16 <  - s - 6 OR 2s + 5 > 11

s < - 22 OR s > 3

500

Solve:

-15 < 5 ( 3p - 2 ) < 20

- 1/3 < p < 2

Absolute Valie Inequalities

100

Solve:

|y| = 36

y = 36, -36

200

Solve :

| q + 8 | = 2

q = -6, -10

300

Solve:

| b - 5 | < 10

-5 < b < 15

400

Solve:

| 4c + 5 | > 7

c < -3 OR c > 1/2

500

Solve:

| t | > 3

t < - 3 OR t > 3

Linear Inequalities

100

Is it a solution?

x + y < 4

(0,0)

Not a Solution

200

Is it a solution?

y < 8

(10, 7)

Yes it is a Solution

300

Graph:

y > x + 3

Check graphs...

400

Graph:

y < - 3

Check

500

Graph:

- 4y < 16x

Check