The document discusses how to solve simple and compound inequalities. It explains that solving inequalities follows the same process as solving equations, but requires paying attention to the inequality sign and graphing the solution set. It provides examples of solving different types of inequalities, such as those with addition, subtraction, multiplication, and division, noting that the inequality sign may need to be reversed when multiplying or dividing by a negative number.

1. Solving Inequalities
Today’s objective:
1. I will solve simple and
compound inequalities.

2. Solving Inequalities
● Solving inequalities follows the same
procedures as solving equations.
● There are a few special things to
consider with inequalities:
● We need to look carefully at the inequality sign.
● We also need to graph the solution set.

3. Review of Inequality Signs
> greater than
< less than
≥ greater than or equal
≤ less than or equal

4. How to graph the solutions
> Graph any number greater than. . .
open circle, line to the right
< Graph any number less than. . .
open circle, line to the left
≥ Graph any number greater than or equal to. . .
closed circle, line to the right
≤ Graph any number less than or equal to. . .
closed circle, line to the left

5. Solve the inequality:
x+4<7
-4 -4 ●Subtract 4 from each side.
●Keep the same inequality sign.
x < 3
●Graph the solution.
• Open circle, line to the left.
0 3

6. 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.

7. Example:
Solve: -3y + 5 >23
●Subtract 5 from each side.
-5 -5
-3y > 18
-3 -3 ●Divide each side by negative 3.
y < -6 ●Reverse the inequality sign.
●Graph the solution.
•Open circle, line to the left.
-6 0

8. Try these:
● Solve 2x+3>x+5
● Answer: x > 2
● Solve - c - 11>23
● Answer: c < -34
● Solve 3(r-2)<2r+4
● Answer: x < 10