Finite Math Examples

Convert to Interval Notation |7x|<42
Step 1
Write as a piecewise.
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Step 1.1
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Step 1.2
Divide each term in by and simplify.
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Step 1.2.1
Divide each term in by .
Step 1.2.2
Simplify the left side.
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Step 1.2.2.1
Cancel the common factor of .
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Step 1.2.2.1.1
Cancel the common factor.
Step 1.2.2.1.2
Divide by .
Step 1.2.3
Simplify the right side.
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Step 1.2.3.1
Divide by .
Step 1.3
In the piece where is non-negative, remove the absolute value.
Step 1.4
To find the interval for the second piece, find where the inside of the absolute value is negative.
Step 1.5
Divide each term in by and simplify.
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Step 1.5.1
Divide each term in by .
Step 1.5.2
Simplify the left side.
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Step 1.5.2.1
Cancel the common factor of .
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Step 1.5.2.1.1
Cancel the common factor.
Step 1.5.2.1.2
Divide by .
Step 1.5.3
Simplify the right side.
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Step 1.5.3.1
Divide by .
Step 1.6
In the piece where is negative, remove the absolute value and multiply by .
Step 1.7
Write as a piecewise.
Step 2
Solve when .
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Step 2.1
Divide each term in by and simplify.
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Step 2.1.1
Divide each term in by .
Step 2.1.2
Simplify the left side.
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Step 2.1.2.1
Cancel the common factor of .
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Step 2.1.2.1.1
Cancel the common factor.
Step 2.1.2.1.2
Divide by .
Step 2.1.3
Simplify the right side.
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Step 2.1.3.1
Divide by .
Step 2.2
Find the intersection of and .
Step 3
Solve when .
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Step 3.1
Divide each term in by and simplify.
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Step 3.1.1
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.
Step 3.1.2
Simplify the left side.
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Step 3.1.2.1
Cancel the common factor of .
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Step 3.1.2.1.1
Cancel the common factor.
Step 3.1.2.1.2
Divide by .
Step 3.1.3
Simplify the right side.
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Step 3.1.3.1
Divide by .
Step 3.2
Find the intersection of and .
Step 4
Find the union of the solutions.
Step 5
Convert the inequality to interval notation.
Step 6