Solving one step Inequalities

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An inequality is like an equation, but instead of an equal sign (=) it

has one of these signs:

< : less than≤ : less than or equal to

> : greater than≥ : greater than or equal to

What do Inequalities mean?

•A mathematical sentence that uses one of the inequality symbols to state the relationship between two quantities.

Solving an Inequality• Follow the same rules and steps that

we used to solve an equation. •Always undo addition or subtraction

first, then multiplication or division.•Remember whatever is done to one

side of the inequality must be done to the other side. The goal is to get the variable by itself.

- 8 -8

x ≥ 7

Solve x + 8 1 5

1. Draw “the river” to separate the inequality into 2 sides

2. Subtract 8 from both sides

3. Simplify vertically

≥

All numbers greater than 7 (including 7)

- 16 -16

r < -23

You Try r + 16 < -71. Draw “the river” to

separate the inequality into 2 sides

2. Subtract 16 from both sides

3. Simplify verticallyAll numbers less than

-23

0 5 10 15-20 -15 -10 -5-25 20 25

Solve 7 ≥ m - 3 + 3 + 3

10 ≥ m

1. Draw “the river” to separate the inequality into 2 sides

2. Add 3 to both sides3. Simplify vertically4. Put the variable on the left

hand side

= m ≤ 10All numbers less than

10 (including 10)

Solve x - (-2) > 1

x + 2 > 1

- 2 - 2

x > -1

1. Draw “the river” to separate the inequality into 2 sides

2. Eliminate the double sign3. Subtract 2 from both sides4. Simplify vertically

All numbers greater than -1

More Examples10x > -20

10 10

x > -2

All numbers greater than -2 make this problem true!

There is one special case.

●Sometimes you may have to reverse the direction of the inequality sign!!

●That only happens when you

multiply or divide both sides of the inequality by a negative number.

Solve -5t ≥ 20 -5 -5

t ≥ -4

t ≤ -4

1. Draw “the river” to separate the inequality into 2 sides

2. Divide both sides by -5

3. Reverse your inequality sign!

All numbers less than -4 (including -4)

Solve ≥ -6

x ≥ 15

x ≤ 15

1. Draw “the river” to separate the inequality into 2 sides

2. Divide both sides by

by -

3. Reverse your inequality sign!

All numbers less than 15(including 15)

- ≥ -6 ×-

-

0 5 10 15-20 -15 -10 -5-25 20 25

Solve < 2

x < -8

x > -8

1. Draw “the river” to separate the inequality into 2 sides

2. Multiply each side by -4

3. Reverse your inequality sign!

All numbers greater than -8

- < 2 ×-

-