1.5 solving inequalities
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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
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
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
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
SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.
5 1 1 13x and x
SOLVE THE COMPOUND INEQUALITY. GRAPH THE SOLUTION.
3 2 1 11x
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