1. Classify each statement as true or false. If false, explain how to change the inequality to make it true.
a. If x > 9, then -3x > -27.
b. If x < 4, then 3x < 12.
2. Complete each statement.
a. If each side of an inequality is multiplied by the same ______ number, the direction of the inequality symbol must be reversed so that the resulting inequality is true.
b. Multiplying by _______ is the same as dividing by -6.
c. An acute triangle has angles whose measures are all less than _____________.
3. You Decide Utina and Paige are discussing the rules for changes in the direction of the inequality symbol when solving inequalities. Paige says the rule is "Whenever you have a negative sign in the problem, the direction of the inequality will change." Utina says that is not always true. Decide who is correct and give examples to support your answer.
Use models to solve each inequality. Write the answer in set-builder notation.
4. 3x < 15
5. 2x + 6 > x - 7
6. Use models to determine the appropriate symbol (>, <, or =) to complete each comparison.
a. x + 5 ____ x - 7
b. x + 3 + (x - 6) _____ (2x + 7) - 4
c. 2x + 8 _____ 2x + 6 - x
State the number by which you multiply or divide to solve each inequality. Indicate whether the direction of the inequality symbol reverses. Then solve.
7. 10x > 20
8. x/4 < -5
Solve each inequality. Then check your solution.
9. (4/5)x < 24
10. 5y > -25