1. Bell Work 9/15/17
Solve the Inequalities for x and give two possible solutions. (what are some numbers that would work for x?)
1. 2𝑥≤7
2. 3𝑥−2>9

2. Inequalities I can… - Represent an inequality in multiple ways.
- Interpret the solution sets for inequalities.

3. Representing an Inequality
In words
Algebraically
On a Number Line
Set Notation

4. Representing With Words
*Decide which inequality sign goes with the following phrases*
___ At least
___ Fewer than
___ No less than
___ Not above
___ Does not exceed
___ Over
___ Under
___ Is more than
___ Beneath
___ Minimum
___ Greater than ___ Less than ___ Greater than or equal to ___ Less than or equal to ___ Not equal to ___ More than ___ No more than
___ At most
___ Below
___ Above
___ Not under
___ Smaller than
___ Maximum

5. Representing Algebraically
x is less than 8.
x is greater than 8.
x is less than or equal to 8.
x is greater than or equal to 8.
𝑥<8
𝑥>8
𝑥≤8
𝑥≥8

6. Represent With a Number Line
Change the number line notation to algebraic notation 1. 2. 3. 4.

7. Representing With Set Notation
**Set Notation shows the beginning and ending numbers for an inequality**

8. Set Notation
What do the following sets look like algebraically?

9. Set Notation 𝑥<8 2. ________ ________ 3. 𝑥 is less than 5 ________
Write the following representations in Set Notation.
𝑥<8
________ 2.
________
3. 𝑥 is less than 5
________

10. Solutions to Inequalities
Things to think about.
When you multiply or divide by a negative.
When the variables cancel.

11. Multiply or Divide By A Negative
**If you multiply or divide by a negative number, you MUST change the direction of the inequality**
Solve the following inequalities for x.
−2𝑥≤4
−3𝑥−2>10
−𝑥<−2

12. What to Do When the Variables Cancel Out
If you end with a true statement, the solution is “ALL REAL NUMBERS”.
Ex. 5 > 0
If you end with a false statement, there is “NO SOLUTION”.
Ex. 10 < 2
2𝑚<2𝑚+3
2𝑚>2𝑚+3
5𝑥+7≥5𝑥−2
2(𝑛+1)≤2𝑛