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Algebra Examples
Step 1
Step 1.1
To find the interval for the first piece, find where the inside of the absolute value is non-negative.
Step 1.2
Add to both sides of the inequality.
Step 1.3
In the piece where is non-negative, remove the absolute value.
Step 1.4
To find the interval for the second piece, find where the inside of the absolute value is negative.
Step 1.5
Add to both sides of the inequality.
Step 1.6
In the piece where is negative, remove the absolute value and multiply by .
Step 1.7
Write as a piecewise.
Step 1.8
Subtract from .
Step 1.9
Simplify .
Step 1.9.1
Simplify each term.
Step 1.9.1.1
Apply the distributive property.
Step 1.9.1.2
Multiply by .
Step 1.9.2
Add and .
Step 2
Step 2.1
Add to both sides of the inequality.
Step 2.2
Add and .
Step 3
Step 3.1
Move all terms not containing to the right side of the inequality.
Step 3.1.1
Add to both sides of the inequality.
Step 3.1.2
Add and .
Step 3.2
Divide each term in by and simplify.
Step 3.2.1
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 3.2.2
Simplify the left side.
Step 3.2.2.1
Dividing two negative values results in a positive value.
Step 3.2.2.2
Divide by .
Step 3.2.3
Simplify the right side.
Step 3.2.3.1
Divide by .
Step 4
Find the union of the solutions.
or
Step 5
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
Step 6