Trigonometry Examples

Solve for x 1/2*(x+3)+2(x-4)>1/3*(x-3)
Step 1
Simplify .
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Step 1.1
Simplify each term.
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Step 1.1.1
Apply the distributive property.
Step 1.1.2
Combine and .
Step 1.1.3
Combine and .
Step 1.1.4
Apply the distributive property.
Step 1.1.5
Multiply by .
Step 1.2
To write as a fraction with a common denominator, multiply by .
Step 1.3
Combine and .
Step 1.4
Combine the numerators over the common denominator.
Step 1.5
Combine the numerators over the common denominator.
Step 1.6
Multiply by .
Step 1.7
Add and .
Step 1.8
To write as a fraction with a common denominator, multiply by .
Step 1.9
Simplify terms.
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Step 1.9.1
Combine and .
Step 1.9.2
Combine the numerators over the common denominator.
Step 1.10
Simplify the numerator.
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Step 1.10.1
Multiply by .
Step 1.10.2
Add and .
Step 2
Simplify .
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Step 2.1
Apply the distributive property.
Step 2.2
Combine and .
Step 2.3
Cancel the common factor of .
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Step 2.3.1
Factor out of .
Step 2.3.2
Cancel the common factor.
Step 2.3.3
Rewrite the expression.
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
To write as a fraction with a common denominator, multiply by .
Step 3.3
To write as a fraction with a common denominator, multiply by .
Step 3.4
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Step 3.4.1
Multiply by .
Step 3.4.2
Multiply by .
Step 3.4.3
Multiply by .
Step 3.4.4
Multiply by .
Step 3.5
Combine the numerators over the common denominator.
Step 3.6
Simplify the numerator.
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Step 3.6.1
Apply the distributive property.
Step 3.6.2
Multiply by .
Step 3.6.3
Multiply by .
Step 3.6.4
Multiply by .
Step 3.6.5
Subtract from .
Step 3.6.6
Factor out of .
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Step 3.6.6.1
Factor out of .
Step 3.6.6.2
Factor out of .
Step 3.6.6.3
Factor out of .
Step 4
Multiply both sides by .
Step 5
Simplify.
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Step 5.1
Simplify the left side.
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Step 5.1.1
Simplify .
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Step 5.1.1.1
Cancel the common factor of .
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Step 5.1.1.1.1
Cancel the common factor.
Step 5.1.1.1.2
Rewrite the expression.
Step 5.1.1.2
Apply the distributive property.
Step 5.1.1.3
Multiply by .
Step 5.2
Simplify the right side.
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Step 5.2.1
Multiply by .
Step 6
Solve for .
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Step 6.1
Move all terms not containing to the right side of the inequality.
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Step 6.1.1
Add to both sides of the inequality.
Step 6.1.2
Add and .
Step 6.2
Divide each term in by and simplify.
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Step 6.2.1
Divide each term in by .
Step 6.2.2
Simplify the left side.
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Step 6.2.2.1
Cancel the common factor of .
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Step 6.2.2.1.1
Cancel the common factor.
Step 6.2.2.1.2
Divide by .
Step 7
The result can be shown in multiple forms.
Inequality Form:
Interval Notation: