# Inequalities

**Chapter 3.3--Inequalities**

Inequalities are like equations except that in the place
of = we use <,>, ≤, or ≥ .

Treat inequalities exactly as you treat equations , with one important exception.
If you multiply the inequality by a negative number, then you must reverse the
inequality.

**Part 1 Graphing inequalities .
**The graph will be done on the board.

**Question 3** Graph

x≤0

**Question 4** Graph

x < 4

**Question 12 **Solve and Graph

Subtract 5 from both sides

x≥−2

**Part 2 Solving inequalities **

**Question 18:** Solve

Subtract 8 from both sides x≥−22

**Question 42**: Solve

Subtract 2.8x from both sides x < −3.8

If you want to be really proper you can write the solution as

**Question 59:** Solve −8x ≤ −40

Divide both sides by −8 : [Remember that since we are multiplying/dividing by a negative number that we must reverse the inequality.] x≥5

**Question 93: **Solve 0.07x < −0.378

Divide by 0.07

So the solution is x < −5.4

**Question 124: **Solve:

First we simplify by removing parentheses on both sides.

Collect ( Combine ) like terms on each side

10−4y≤6y−20

Subtract 6y from both sides: 10−10y≤−20

Subtract 10 from both sides: −10y≤−30

Divide both sides by −10 . Reverse the inequality.

y≥3

**Question 134: **Use the roster method to list the set
of positive integers that are solutions of the inequality 13−8a≥2−6a

First we solve the inequality :

Add 8a to both sides:

Subtract 2. 11≥2a

Divide by 2 .

Roster method gives us
because , we can’t go any higher than 5.

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