Inequalities

Equation Inequality

A statement that asserts the equality of 2 terms

A relationship between 2 terms that are of unequal value

Contains an equal sign = equal to

Contains an inequality sign< less than

> Greater than≤ less than or equal to

≥ greater than or equal to

Solution is one numberX + 5 = 10X = 5

Solution is more than one numberX + 5 < 10X < 5

Solution is represented by a single dot on the number line

Solution is represented by a solid or hollow dot and and arrow

Inequalities

<Smaller value

Larger value

10 20

Inequalities

<Larger value

Smaller value

20 10

Inequalities<= ≥

Greater than

Equal to

Greater than or equal to

Inequalities

<= ≤

Less than

Equal to

Less than or equal to

Inequalities

≤xX is less than or equal to 5

5

5Solid Dot

All numbers

that are less

than or equal

to 5

Include 5 because x is less than or equal to 5

Line goes to the left because x is less than or equal to 5

Inequalities

<xX is less than 5

5

5Hollow Dot

All numbers

that are less

than 5

Does not include 5 because x is only less than 5

Line goes to the left because x is less than 5

Inequalities

≥xX is greater than or equal to 5

5

5

Solid Dot

All numbers that

are greater than

or equal to 5

Include 5 because x is greater than or equal to 5

Line goes to the right because x is greater than or equal to 5

Inequalities

>xX is greater than 5

5

5

Hollow Dot

All numbers that

are greater than 5

Does not include 5 because x is only greater than 5

Line goes to the right because x is greater than 5

Inequalities

-2 0 2 4 6-4-6

X ≥ 0

Inequalities

-2 0 2 4 6-4-6

X > 4

Inequalities

-2 0 2 4 6-4-6

X ≤ -2

Inequalities

-2 0 2 4 6-4-6

X < 6

Inequalities

-2 0 2 4 6-4-6

X > -6

Inequalities6 > x

Rewrite inequalities so that the variable is on

the left

x 6<If you switch

sides, the

inequality sign

needs to be

flipped

6 is greater than x

x is less than 6

Inequalities

10 > x

Rewrite with the variable on the left:

x < 10n ≤ -6

-5 < y

-6 ≥ n y > -5

Inequalities

10 > x +5

Rewrite with the variable on the left:

x + 5 < 10

n - 6 ≤ -6

-5 < 5y -6

-6 ≥ n - 6 5y – 6 > -5

Solving One Step Inequalitiesx + 7 < 4

- 7 -7

x < -3

Solving One Step Inequalities-5 ≥ x +

8

- 8 -8

x ≤ -13

x + 8 ≤ -5

Rewrite so that x is on the left, be sure to flip inequality sign

Solving One Step Inequalitiesx – 10 > -4 + 10 +10

x > 6

Solving One Step Inequalities -1 < x – 10

+ 10 +10 x >

9

x – 10 > -1 Rewrite so that x is on the left, be sure to flip inequality sign

Solving One Step Inequalities 2x ≥ 10 2 2 x ≥ 5

Solving One Step Inequalities -2x ≥ 10 -2 -2 x ≤ -5

When multiplying or dividing by a negative, the inequality sign must be flipped

Solving Two Step Inequalities

3x + 7 ≥ 10 -7 -7

3x ≥ 3 3 3 x ≥ 1

Solving Two Step Inequalities

-4x - 1 < 7 +1 +1

-4x < 8 -4 -4 x > -2

When multiplying or dividing by a negative, the inequality sign must be flipped

Solving Two Step Inequalities

x + 5 > 11 2 -5 -

5x > 62

x > 12

x > 6 2

(2)

(2)

Solving Two Step Inequalities x - 5 ≤ -2 -3

+5 +5 x ≤

3 -3

x ≥ -9

x ≤ 3 -3

When multiplying or dividing by a negative, the inequality sign must be flipped

(-3) (-3)

Solving Two Step Inequalities -5 > 5x + 10

-10 -10 5x < -15

5 5 x < -3

5x + 10 < -5 Rewrite so that x is on the left, be sure to flip inequality sign