Finite Math Examples

Convert to Interval Notation 1/5b+3/4b-1/8>1/8*(b+1)+b
Step 1
Simplify .
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Step 1.1
Simplify each term.
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Step 1.1.1
Combine and .
Step 1.1.2
Combine and .
Step 1.2
To write as a fraction with a common denominator, multiply by .
Step 1.3
To write as a fraction with a common denominator, multiply by .
Step 1.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 1.4.1
Multiply by .
Step 1.4.2
Multiply by .
Step 1.4.3
Multiply by .
Step 1.4.4
Multiply by .
Step 1.5
Combine the numerators over the common denominator.
Step 1.6
Simplify each term.
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Step 1.6.1
Simplify the numerator.
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Step 1.6.1.1
Factor out of .
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Step 1.6.1.1.1
Factor out of .
Step 1.6.1.1.2
Factor out of .
Step 1.6.1.1.3
Factor out of .
Step 1.6.1.2
Multiply by .
Step 1.6.1.3
Add and .
Step 1.6.2
Move to the left of .
Step 2
Simplify .
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Step 2.1
Simplify each term.
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Step 2.1.1
Apply the distributive property.
Step 2.1.2
Combine and .
Step 2.1.3
Multiply by .
Step 2.2
To write as a fraction with a common denominator, multiply by .
Step 2.3
Simplify terms.
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Step 2.3.1
Combine and .
Step 2.3.2
Combine the numerators over the common denominator.
Step 2.3.3
Combine the numerators over the common denominator.
Step 2.4
Move to the left of .
Step 2.5
Add and .
Step 3
Move all terms containing to the left side of the inequality.
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Step 3.1
Subtract from both sides of the inequality.
Step 3.2
Combine the numerators over the common denominator.
Step 3.3
Simplify each term.
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Step 3.3.1
Apply the distributive property.
Step 3.3.2
Multiply by .
Step 3.3.3
Multiply by .
Step 3.4
Subtract from .
Step 3.5
To write as a fraction with a common denominator, multiply by .
Step 3.6
To write as a fraction with a common denominator, multiply by .
Step 3.7
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.7.1
Multiply by .
Step 3.7.2
Multiply by .
Step 3.7.3
Multiply by .
Step 3.7.4
Multiply by .
Step 3.8
Combine the numerators over the common denominator.
Step 3.9
Simplify the numerator.
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Step 3.9.1
Multiply by .
Step 3.9.2
Apply the distributive property.
Step 3.9.3
Multiply by .
Step 3.9.4
Multiply by .
Step 3.9.5
Subtract from .
Step 3.10
Factor out of .
Step 3.11
Rewrite as .
Step 3.12
Factor out of .
Step 3.13
Rewrite as .
Step 3.14
Move the negative in front of the fraction.
Step 4
Divide each term in by and simplify.
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Step 4.1
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 4.2
Simplify the left side.
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Step 4.2.1
Dividing two negative values results in a positive value.
Step 4.2.2
Divide by .
Step 4.3
Simplify the right side.
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Step 4.3.1
Divide by .
Step 5
Multiply both sides by .
Step 6
Simplify.
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Step 6.1
Simplify the left side.
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Step 6.1.1
Cancel the common factor of .
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Step 6.1.1.1
Cancel the common factor.
Step 6.1.1.2
Rewrite the expression.
Step 6.2
Simplify the right side.
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Step 6.2.1
Multiply by .
Step 7
Solve for .
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Step 7.1
Subtract from both sides of the inequality.
Step 7.2
Divide each term in by and simplify.
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Step 7.2.1
Divide each term in by .
Step 7.2.2
Simplify the left side.
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Step 7.2.2.1
Cancel the common factor of .
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Step 7.2.2.1.1
Cancel the common factor.
Step 7.2.2.1.2
Divide by .
Step 7.2.3
Simplify the right side.
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Step 7.2.3.1
Move the negative in front of the fraction.
Step 8
Convert the inequality to interval notation.
Step 9