In the previous lesson, you learned that addition and subtraction inequalities are solved with the same procedures as addition and subtraction equations. Can you use the procedures for solving multiplication and division equations to solve inequalities as well?
For example, to solve 4x = 36, we would divide each
side by 4. Will this work when solving inequalities? Consider the inequality 4 <
36.
So, it is possible to solve an inequality when dividing by a
positive number. What happens when you divide by a negative number? Consider the
inequality –4 < 36.
When dividing by a negative number, you must reverse the symbol
for the inequality to remain true. This example leads us to the Division Property
for Inequalities.
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1. Carmen runs at least 15 miles in the
park every day. If she runs 5 miles per hour, how long does she run every day?
Recall that rate times time equals distance, or rt = d.
Alternative Solutions:
Carmen runs
at least 3 hours every day.
2.
Solve –10x ≤ 25.6. Check your solution.
Alternative Solutions:
Check: Substitute 2.56 and a number greater
than 2.56, such as 0,
into the inequality.
The solution set is {x│x ≤ 2.56}.
We can also solve inequalities by
multiplying. Use the Multiplication Property for Inequalities.
Example
Alternative Solutions:
Check: Substitute 18 and a number greater
than 18,
such as
21, into the inequality.
The solution is {x│x >
18}.
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