1. 1.5 SOLVING INEQUALITIES

2. INEQUALITIES
 An inequality is a relationship in which two
quantities may not be equal.
 Phrases such as “at most” and “at least” suggest this
type of relationship

3. WRITING & GRAPHING
INEQUALITIES

4. WRITE THE INEQUALITY
THAT REPRESENTS THE
SENTENCE.
 5 fewer than a number is at least 12
 The product of a number and 8 is greater than 25
 The quotient of a number and 3 is no more than
15

5. SOLVING INEQUALITIES
 The solutions of an inequality are the numbers
(values) that make it true.
 We solve inequalities the same way we solve
equations
 Except:when we multiply or divide by a negative
number, we reverse the inequality symbol
 Hint: when you solve, put the variable on the LEFT,
this ensures that the arrow on the graph points the
same way as the pointed end of the inequality symbol

6. SOLVE EACH INEQUALITY.
GRAPH THE SOLUTION.
2x > 8

7. SOLVE EACH INEQUALITY.
GRAPH THE SOLUTION.
12 − 2 y ≥ 38

8. SOLVE EACH INEQUALITY.
GRAPH THE SOLUTION.
5 ( x + 3) ≤ 55

9. SOLVE EACH INEQUALITY.
GRAPH THE SOLUTION.
−2 ( w + 4 ) + 9 < −13

10. NO SOLUTION OR ALL REAL
NUMBERS AS SOLUTIONS
 When solving inequalities, we can reach solutions
that seem strange and require analysis.
 If we reach a false statement, there are no solutions,
and the statement is never true
 If the variable(s) drop out and we have a true
statement or we reach a point where one side is
identical to the other, the statement is always true
for all real numbers.

11. IS THE INEQUALITY ALWAYS,
SOMETIMES, OR NEVER
TRUE?
3 ( x + 5 ) < 30

12. IS THE INEQUALITY ALWAYS,
SOMETIMES, OR NEVER
TRUE?
−2 ( 3 x + 1) > −6 x + 7

13. IS THE INEQUALITY ALWAYS,
SOMETIMES, OR NEVER
TRUE?
5 ( 2 x − 3) − 7 x ≤ 3 x + 8

14. COMPOUND INEQUALITIES
 A compound inequality is an inequality
statement that joins two inequalities using the
word and or the word or.

15. COMPOUND INEQUALITIES
 To solve a compound inequality containing and:
 Find all values of the variable that make both
inequalities true

16. SOLVE THE COMPOUND
INEQUALITY. GRAPH THE
SOLUTION.
7 < 2 x + 1 and 3 x ≤ 18

17. SOLVE THE COMPOUND
INEQUALITY. GRAPH THE
SOLUTION.
3 < 2 x + 1 < 11 This is a collapsed
“and inequality”

18. COMPOUND INEQUALITIES
 To solve a compound inequality containing or:
 Find all values of the variable that make at least one
of the inequalities true.

19. SOLVE THE COMPOUND
INEQUALITY. GRAPH THE
SOLUTION.
7 + k ≥ 6 or 8 + k < 3

20. SOLVE THE COMPOUND
INEQUALITY. GRAPH THE
SOLUTION.
7 w + 3 > 11 or 4 w − 1 < −13

21. HOMEWORK
 Page 38
 #11– 23, 29 – 43, 45 – 49, 59 – 61
odds only