Inequalities: Solving and Graphing

• Mathematics
• 9th,10th Grade

Inequalities

What does each of the following symbols mean
a. > b. ˂ c. ≤ d. ≥

Example: 

                       -3x ˂ 12

 1. (-3x) / (-3)  <  12  /  (-3)      Divide   

                            x < -4                           

    

 2.  x > -4              *Reverse symbol

 3.  {𝑥: 𝑥 > −4}   Write notation.

                                                              

Solving Inequalities

1. Isolate the variable term by multiplying or dividing.

*When you multiply or divide by a negative number then reverse the inequality symbol.* 

2. Reverse symbol. 

3. Write the notation  set.

Solve: 7x ˂ 28

1. x ˃ -4
2. x ˂ 4
3. x ˃ 4
4. x ˂ -4

Graphing Inequalities

           1. Determine if you use a closed circle or open circle.

Remember: closed circle - equals to; open circle- not equal

           2. Is the sign greater or less than

           3. Graph the inequality

Example:   

          x > -4                                                                                                       

-4x < 12

1. x ˂ -3
2. x > 3
3. x > -3
4. x ˂ 3

WHAT I NOW KNOW

At the end of this lesson you should know:

1. how to algebraically solve an inequality 

2. how to graph the solution of the inequality