1.5

1.5 SOLVING INEQUALITIES

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

WRITING & GRAPHING INEQUALITIES

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

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

SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.

2 8x

SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.

12 2 38y

SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.

5 3 55x

SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.

2 4 9 13w

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.

IS THE INEQUALITY ALWAYS, SOMETIMES, OR NEVER TRUE?

3 5 30x

IS THE INEQUALITY ALWAYS, SOMETIMES, OR NEVER TRUE?

2 3 1 6 7x x

IS THE INEQUALITY ALWAYS, SOMETIMES, OR NEVER TRUE?

5 2 3 7 3 8x x x

COMPOUND INEQUALITIES A compound inequality is an inequality

statement that joins two inequalities using the word and or the word or.

COMPOUND INEQUALITIES To solve a compound inequality containing

and: Find all values of the variable that make both

inequalities true

SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.

7 2 1 3 18x and x

SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.3 2 1 11x This is a

collapsed “and inequality”

COMPOUND INEQUALITIES To solve a compound inequality containing

or: Find all values of the variable that make at least

one of the inequalities true.

SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.7 6 8 3k or k

SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.7 3 11 4 1 13w or w

HOMEWORK Page 38

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