Finite Math Examples

Solve for a 5-3/a<7/a
Step 1
Multiply both sides by .
Step 2
Simplify.
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Step 2.1
Simplify the left side.
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Step 2.1.1
Simplify .
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Step 2.1.1.1
Apply the distributive property.
Step 2.1.1.2
Cancel the common factor of .
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Step 2.1.1.2.1
Move the leading negative in into the numerator.
Step 2.1.1.2.2
Cancel the common factor.
Step 2.1.1.2.3
Rewrite the expression.
Step 2.2
Simplify the right side.
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Step 2.2.1
Cancel the common factor of .
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Step 2.2.1.1
Cancel the common factor.
Step 2.2.1.2
Rewrite the expression.
Step 3
Solve for .
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Step 3.1
Move all terms not containing to the right side of the equation.
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Step 3.1.1
Add to both sides of the equation.
Step 3.1.2
Add and .
Step 3.2
Divide each term in by and simplify.
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Step 3.2.1
Divide each term in by .
Step 3.2.2
Simplify the left side.
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Step 3.2.2.1
Cancel the common factor of .
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Step 3.2.2.1.1
Cancel the common factor.
Step 3.2.2.1.2
Divide by .
Step 3.2.3
Simplify the right side.
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Step 3.2.3.1
Divide by .
Step 4
Find the domain of .
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Step 4.1
Set the denominator in equal to to find where the expression is undefined.
Step 4.2
The domain is all values of that make the expression defined.
Step 5
Use each root to create test intervals.
Step 6
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
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Step 6.1
Test a value on the interval to see if it makes the inequality true.
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Step 6.1.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 6.1.2
Replace with in the original inequality.
Step 6.1.3
The left side is not less than the right side , which means that the given statement is false.
False
False
Step 6.2
Test a value on the interval to see if it makes the inequality true.
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Step 6.2.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 6.2.2
Replace with in the original inequality.
Step 6.2.3
The left side is less than the right side , which means that the given statement is always true.
True
True
Step 6.3
Test a value on the interval to see if it makes the inequality true.
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Step 6.3.1
Choose a value on the interval and see if this value makes the original inequality true.
Step 6.3.2
Replace with in the original inequality.
Step 6.3.3
The left side is not less than the right side , which means that the given statement is false.
False
False
Step 6.4
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
False
True
False
Step 7
The solution consists of all of the true intervals.
Step 8
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 9