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Algebra Examples
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Step 1
Step 1.1
Divide each term in by and simplify.
Step 1.1.1
Divide each term in by . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.
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Step 1.1.2
Simplify the left side.
Step 1.1.2.1
Dividing two negative values results in a positive value.
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Step 1.1.2.2
Divide by .
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Step 1.1.3
Simplify the right side.
Step 1.1.3.1
Divide by .
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Step 1.2
Multiply both sides by .
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Step 1.3
Simplify.
Step 1.3.1
Simplify the left side.
Step 1.3.1.1
Cancel the common factor of .
Step 1.3.1.1.1
Cancel the common factor.
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Step 1.3.1.1.2
Rewrite the expression.
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Step 1.3.2
Simplify the right side.
Step 1.3.2.1
Multiply by .
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Step 1.4
Divide each term in by and simplify.
Step 1.4.1
Divide each term in by .
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Step 1.4.2
Simplify the left side.
Step 1.4.2.1
Cancel the common factor of .
Step 1.4.2.1.1
Cancel the common factor.
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Step 1.4.2.1.2
Divide by .
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Step 1.4.3
Simplify the right side.
Step 1.4.3.1
Divide by .
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Step 2
Step 2.1
Move all terms not containing to the right side of the inequality.
Step 2.1.1
Subtract from both sides of the inequality.
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Step 2.1.2
Subtract from .
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Step 2.2
Divide each term in by and simplify.
Step 2.2.1
Divide each term in by .
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Step 2.2.2
Simplify the left side.
Step 2.2.2.1
Cancel the common factor of .
Step 2.2.2.1.1
Cancel the common factor.
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Step 2.2.2.1.2
Divide by .
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Step 2.2.3
Simplify the right side.
Step 2.2.3.1
Move the negative in front of the fraction.
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Step 3
The intersection consists of the elements that are contained in both intervals.
Step 4
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 5