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Algebra Examples
Step 1
Multiply both sides by .
Step 2
Step 2.1
Simplify the left side.
Step 2.1.1
Cancel the common factor of .
Step 2.1.1.1
Cancel the common factor.
Step 2.1.1.2
Rewrite the expression.
Step 2.2
Simplify the right side.
Step 2.2.1
Simplify .
Step 2.2.1.1
Apply the distributive property.
Step 2.2.1.2
Cancel the common factor of .
Step 2.2.1.2.1
Factor out of .
Step 2.2.1.2.2
Factor out of .
Step 2.2.1.2.3
Cancel the common factor.
Step 2.2.1.2.4
Rewrite the expression.
Step 2.2.1.3
Combine and .
Step 2.2.1.4
Multiply .
Step 2.2.1.4.1
Multiply by .
Step 2.2.1.4.2
Combine and .
Step 2.2.1.5
Simplify each term.
Step 2.2.1.5.1
Move to the left of .
Step 2.2.1.5.2
Move the negative in front of the fraction.
Step 3
Step 3.1
Move all terms containing to the left side of the inequality.
Step 3.1.1
Subtract from both sides of the inequality.
Step 3.1.2
To write as a fraction with a common denominator, multiply by .
Step 3.1.3
Combine and .
Step 3.1.4
Combine the numerators over the common denominator.
Step 3.1.5
Subtract from .
Step 3.1.5.1
Reorder and .
Step 3.1.5.2
Subtract from .
Step 3.1.6
Move the negative in front of the fraction.
Step 3.2
Move all terms not containing to the right side of the inequality.
Step 3.2.1
Add to both sides of the inequality.
Step 3.2.2
To write as a fraction with a common denominator, multiply by .
Step 3.2.3
Combine and .
Step 3.2.4
Combine the numerators over the common denominator.
Step 3.2.5
Simplify the numerator.
Step 3.2.5.1
Multiply by .
Step 3.2.5.2
Add and .
Step 3.2.6
Move the negative in front of the fraction.
Step 3.3
Since the expression on each side of the equation has the same denominator, the numerators must be equal.
Step 3.4
Divide each term in by and simplify.
Step 3.4.1
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 3.4.2
Simplify the left side.
Step 3.4.2.1
Cancel the common factor of .
Step 3.4.2.1.1
Cancel the common factor.
Step 3.4.2.1.2
Divide by .
Step 3.4.3
Simplify the right side.
Step 3.4.3.1
Divide by .
Step 4
The result can be shown in multiple forms.
Inequality Form:
Interval Notation: