1. ≤ < > ≥ Solving Inequalities by Multiplying or Dividing
Less than or equal to
Less than ≤
<
greater than
greater than or equal to
> ≥

2. Students solve multistep problems, including word problems, involving linear equations and linear inequalities in one variable and provide justification for each step.

4. Inequalities and their Graphs
Terms you see and need to know to graph inequalities correctly
≤ is less than or equal to
≥ is greater than or equal to
Notice colored in circles

5. Terms you see and need to know to graph inequalities correctly
Inequalities and their Graphs
Terms you see and need to know to graph inequalities correctly
< is less than
Notice open circles
> is greater than

6. Solving Inequalities Using Multiplication
x  -2 3
x  -6
Translation: x divided by 3 is greater than or equal to negative 2.
The opposite of divided by 3 is Multiplying by 3.
What you do on one side you do on the other!
• 3
3 •
Graph -6 -4 -2 4

7. Solving Inequalities Using Division
Translation: 3times x is less than or equal to 12.
The opposite of multiplying by 3 is divided by 3.
What you do on one side you do on the other!
3x ≤ 12 3 1 3
x ≤ 4
Graph -4 -2 2 4

8. Solve the inequality. Then graph the solution.

9. Multiplying and Dividing Inequalities by a Negative Number
Solve the inequality.
12 > -3m
4 < m
Step1: solve for m
-divide by -3
Step 2: reverse the inequality symbol
12 > -3m
< -3 -3
When multiplying or dividing by a negative number reverse the inequality symbol.

10. Solve the inequality. k < -3 -2. .-2 -2 k > 6 >
Multiplying and Dividing Inequalities by a Negative Number
Solve the inequality.
k < -3
Step1: solve for k
-Multiply by -2
Step 2: reverse the inequality symbol
-2.
.-2 -2
k > 6
>
When multiplying or dividing by a negative number reverse the inequality symbol.

11. Tell whether the operation reverses the sign of the inequality.
Multiply each side by -1
Multiply each side b
3) Divide each side by 4.
4) Divide each side by -5.

12. You try: Solve the Inequalities