Children under 12 can enter the museum at no charge. Write the inequality x < 12 If you are 12 can you get in free? no If you are 11 can you get in free?

Children under 12 can enter the museum at no charge.

Write the inequality x < 12If you are 12 can you get in free?n

oIf you are 11 can you get in free? yes

If you are 5 can you get in free?

yes

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

x + 8 1 51. 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)

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 ≤ 10

All 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 sides

4. 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 < 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

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