Precalculus Examples

Solve for x (3x-1)/4-(x-5)/5>-2
Step 1
Simplify .
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Step 1.1
To write as a fraction with a common denominator, multiply by .
Step 1.2
To write as a fraction with a common denominator, multiply by .
Step 1.3
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.3.1
Multiply by .
Step 1.3.2
Multiply by .
Step 1.3.3
Multiply by .
Step 1.3.4
Multiply by .
Step 1.4
Combine the numerators over the common denominator.
Step 1.5
Simplify the numerator.
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Step 1.5.1
Apply the distributive property.
Step 1.5.2
Multiply by .
Step 1.5.3
Multiply by .
Step 1.5.4
Apply the distributive property.
Step 1.5.5
Multiply by .
Step 1.5.6
Apply the distributive property.
Step 1.5.7
Multiply by .
Step 1.5.8
Multiply by .
Step 1.5.9
Subtract from .
Step 1.5.10
Add and .
Step 2
Multiply both sides by .
Step 3
Simplify.
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Step 3.1
Simplify the left side.
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Step 3.1.1
Cancel the common factor of .
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Step 3.1.1.1
Cancel the common factor.
Step 3.1.1.2
Rewrite the expression.
Step 3.2
Simplify the right side.
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Step 3.2.1
Multiply by .
Step 4
Solve for .
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Step 4.1
Move all terms not containing to the right side of the inequality.
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Step 4.1.1
Subtract from both sides of the inequality.
Step 4.1.2
Subtract from .
Step 4.2
Divide each term in by and simplify.
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Step 4.2.1
Divide each term in by .
Step 4.2.2
Simplify the left side.
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Step 4.2.2.1
Cancel the common factor of .
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Step 4.2.2.1.1
Cancel the common factor.
Step 4.2.2.1.2
Divide by .
Step 4.2.3
Simplify the right side.
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Step 4.2.3.1
Divide by .
Step 5
The result can be shown in multiple forms.
Inequality Form:
Interval Notation: