1. ALGEBRA II HONORS/GIFTED - SECTION 1-5 (Solving Inequalities)@
SECTION 1-5 : SOLVING INEQUALITIES

2. Human Number Line activity.
INEQUALITY : A mathematical sentence such that the sides are not equal. Inequalities use one or more of the symbols : Compound inequalities are composed of two or more inequalities.
1) How many solutions can an inequality have?
None, one, infinite!
2) Given 6 < 8, let’s do some…
a) adding
c) multiplying
b) subtracting
d) dividing

3. When you multiply or divide an inequality by a negative number, remember to switch the direction of the inequality.

4. Solve and graph on a number line.
3) 3x – 5 < 16 {real numbers} will always be the solution set.
3x < 21 7
x < 7
< >

5. 4)
-4 •
• -4
j > 16 16

6. 5) x – 3 < or x + 3 > 6
How many parts of an “or” statement must be true for the entire statement to be true?
x < 1 or x > 3
Just
This is a compound inequality because it involves two or more inequalities.
As long as either part is true, GRAPH IT!
So, what is graphed on the number line?
6) 2x – 7 < -11 or -3x + 5 < 3
Both parts!

7. 7) 3 < 2x + 5 < 11
Means 3 < 2x + 5 and 2x + 5 < 11.
Solving this compound inequality in this format gets kind of tricky. Let’s do something different – something us middle children will love!
Solve for x in
the middle.
-2 < 2x < 6
-1 < x < 3
So, where is x located?
Yep, in the middle! So, graph, yep, in the middle.

8. 8) 5 > -3x + 2 > -4
smaller # < x < larger #
larger # > x > smaller #