Linear Inequalities

2x + 3 < 5

2x + 3y < 5

x^2 + 3 < 5

xy + 3 < 5

{1, 2, 3, 4}

{1, 2, 3}

{0, 1, 2, 3}

(-infinity, 4)

x > -3

x < -3

x > 3

x < 3

(-infinity, -1]

(-1, infinity)

[-1, infinity)

(-\infty, \infty)

(1, 1)

(0, 0)

(2, 1)

(1, 0)

Half-plane to the right of x = 3 including the line

Half-plane to the left of x = 3 including the line

Half-plane to the right of x = 3 excluding the line

Only the line x = 3

[-5, 5]

(-5, 5)

(5, infinity)

(-infinity, -5) U (5, infinity)

[-3, 7]

(-3, 7)

(-infinity, -3] U [7, infinity)

[3, 7]

A solid line

A dotted or dashed line

A thick bold line

A curved line

x < 7

x > 7

x <= 7

x >= 7

(2, 5)

[2, 5]

(-infinity, 2] U [5, infinity)

{2, 3, 4, 5}

x > -4

x < -4

x >= -4

x <= -4

False statement

True statement

Undefined

Zero

x >= 2/7

x <= -2/7

x >= -2/7

x <= 2/7

Half-plane above x-axis excluding x-axis

Half-plane below x-axis excluding x-axis

Half-plane to the right of y-axis

The entire Cartesian plane

x > -1

x < -1

x > 1

x < 1

Left half-plane including y-axis

Right half-plane including y-axis

Upper half-plane including x-axis

Lower half-plane including x-axis

Region where x <= 3 and y <= 2

Region where x >= 3 and y >= 2

Region inside a circle of radius 3

A single point (3, 2)

{-1, 0, 1}

{0}

{-1, 0}

{1}

Multiplying both sides by a negative number reverses the inequality sign.

Adding a negative number reverses the inequality sign.

Dividing by any non-zero number reverses the inequality sign.

Subtracting a positive number reverses the inequality sign.