Algebra Examples

Solve for x |x-2|+5<4
Step 1
Write as a piecewise.
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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
Add and .
Step 1.9
Simplify .
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Step 1.9.1
Simplify each term.
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Step 1.9.1.1
Apply the distributive property.
Step 1.9.1.2
Multiply by .
Step 1.9.2
Add and .
Step 2
Solve when .
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Step 2.1
Move all terms not containing to the right side of the inequality.
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Step 2.1.1
Subtract from both sides of the inequality.
Step 2.1.2
Subtract from .
Step 2.2
Find the intersection of and .
No solution
No solution
Step 3
Solve when .
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Step 3.1
Solve for .
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Step 3.1.1
Move all terms not containing to the right side of the inequality.
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Step 3.1.1.1
Subtract from both sides of the inequality.
Step 3.1.1.2
Subtract from .
Step 3.1.2
Divide each term in by and simplify.
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Step 3.1.2.1
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 3.1.2.2
Simplify the left side.
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Step 3.1.2.2.1
Dividing two negative values results in a positive value.
Step 3.1.2.2.2
Divide by .
Step 3.1.2.3
Simplify the right side.
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Step 3.1.2.3.1
Divide by .
Step 3.2
Find the intersection of and .
No solution
No solution
Step 4
Find the union of the solutions.
No solution