Finite Math Examples

Find the Intersection of the Inequalities y<1/2x-2 , y>-2x-1
,
Step 1
Simplify the first inequality.
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Step 1.1
Rewrite so is on the left side of the inequality.
and
Step 1.2
Combine and .
and
Step 1.3
Add to both sides of the inequality.
and
Step 1.4
Multiply both sides by .
and
Step 1.5
Simplify.
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Step 1.5.1
Simplify the left side.
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Step 1.5.1.1
Cancel the common factor of .
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Step 1.5.1.1.1
Cancel the common factor.
and
Step 1.5.1.1.2
Rewrite the expression.
and
and
and
Step 1.5.2
Simplify the right side.
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Step 1.5.2.1
Simplify .
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Step 1.5.2.1.1
Apply the distributive property.
and
Step 1.5.2.1.2
Simplify the expression.
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Step 1.5.2.1.2.1
Move to the left of .
and
Step 1.5.2.1.2.2
Multiply by .
and
and
and
and
and
and
Step 2
Simplify the second inequality.
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Step 2.1
Rewrite so is on the left side of the inequality.
and
Step 2.2
Add to both sides of the inequality.
and
Step 2.3
Divide each term in by and simplify.
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Step 2.3.1
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.
and
Step 2.3.2
Simplify the left side.
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Step 2.3.2.1
Cancel the common factor of .
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Step 2.3.2.1.1
Cancel the common factor.
and
Step 2.3.2.1.2
Divide by .
and
and
and
Step 2.3.3
Simplify the right side.
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Step 2.3.3.1
Simplify each term.
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Step 2.3.3.1.1
Move the negative in front of the fraction.
and
Step 2.3.3.1.2
Move the negative in front of the fraction.
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and
and
and
and
Step 3