1.5 Solving Inequalities

1.5 SOLVING INEQUALITIES

Emily

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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

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

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

SOLVE EACH INEQUALITY. GRAPH THE SOLUTION.

2 8x


12 2 38y


5 3 55x


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


2 3 1 6 7x x


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.


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


To solve a compound inequality containing or: Find all values of the variable that make at least

one of the inequalities true.


7 6 8 3k or k


7 3 11 4 1 13w or w


5 1 1 13x and x


3 2 1 11x

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1.5 Solving Inequalities