Finite Math Examples

Solve for x |x+3|=|4x|-|3x|
Step 1
Since is on the right side of the equation, switch the sides so it is on the left side of the equation.
Step 2
Rewrite the equation as .
Step 3
Solve for .
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Step 3.1
Rewrite the equation as .
Step 3.2
Subtract from both sides of the equation.
Step 3.3
Divide each term in by and simplify.
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Step 3.3.1
Divide each term in by .
Step 3.3.2
Simplify the left side.
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Step 3.3.2.1
Dividing two negative values results in a positive value.
Step 3.3.2.2
Divide by .
Step 3.3.3
Simplify the right side.
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Step 3.3.3.1
Simplify each term.
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Step 3.3.3.1.1
Move the negative one from the denominator of .
Step 3.3.3.1.2
Rewrite as .
Step 3.3.3.1.3
Dividing two negative values results in a positive value.
Step 3.3.3.1.4
Divide by .
Step 4
Remove the absolute value term. This creates a on the right side of the equation because .
Step 5
The result consists of both the positive and negative portions of the .
Step 6
Solve for .
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Step 6.1
Solve for .
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Step 6.1.1
Rewrite the equation as .
Step 6.1.2
Add to both sides of the equation.
Step 6.2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 6.3
The result consists of both the positive and negative portions of the .
Step 6.4
Solve for .
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Step 6.4.1
Solve for .
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Step 6.4.1.1
Rewrite the equation as .
Step 6.4.1.2
Move all terms not containing to the right side of the equation.
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Step 6.4.1.2.1
Subtract from both sides of the equation.
Step 6.4.1.2.2
Subtract from .
Step 6.4.2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 6.4.3
The result consists of both the positive and negative portions of the .
Step 6.4.4
Solve for .
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Step 6.4.4.1
Move all terms containing to the left side of the equation.
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Step 6.4.4.1.1
Subtract from both sides of the equation.
Step 6.4.4.1.2
Combine the opposite terms in .
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Step 6.4.4.1.2.1
Subtract from .
Step 6.4.4.1.2.2
Add and .
Step 6.4.4.2
Since , there are no solutions.
No solution
No solution
Step 6.4.5
Solve for .
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Step 6.4.5.1
Move all terms containing to the left side of the equation.
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Step 6.4.5.1.1
Add to both sides of the equation.
Step 6.4.5.1.2
Add and .
Step 6.4.5.2
Subtract from both sides of the equation.
Step 6.4.5.3
Divide each term in by and simplify.
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Step 6.4.5.3.1
Divide each term in by .
Step 6.4.5.3.2
Simplify the left side.
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Step 6.4.5.3.2.1
Cancel the common factor of .
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Step 6.4.5.3.2.1.1
Cancel the common factor.
Step 6.4.5.3.2.1.2
Divide by .
Step 6.4.5.3.3
Simplify the right side.
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Step 6.4.5.3.3.1
Move the negative in front of the fraction.
Step 6.4.6
Consolidate the solutions.
Step 6.5
Solve for .
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Step 6.5.1
Solve for .
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Step 6.5.1.1
Rewrite the equation as .
Step 6.5.1.2
Simplify .
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Step 6.5.1.2.1
Apply the distributive property.
Step 6.5.1.2.2
Multiply by .
Step 6.5.1.3
Move all terms not containing to the right side of the equation.
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Step 6.5.1.3.1
Add to both sides of the equation.
Step 6.5.1.3.2
Add and .
Step 6.5.1.4
Divide each term in by and simplify.
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Step 6.5.1.4.1
Divide each term in by .
Step 6.5.1.4.2
Simplify the left side.
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Step 6.5.1.4.2.1
Dividing two negative values results in a positive value.
Step 6.5.1.4.2.2
Divide by .
Step 6.5.1.4.3
Simplify the right side.
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Step 6.5.1.4.3.1
Move the negative one from the denominator of .
Step 6.5.1.4.3.2
Rewrite as .
Step 6.5.1.4.3.3
Multiply by .
Step 6.5.2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 6.5.3
The result consists of both the positive and negative portions of the .
Step 6.5.4
Solve for .
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Step 6.5.4.1
Move all terms containing to the left side of the equation.
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Step 6.5.4.1.1
Add to both sides of the equation.
Step 6.5.4.1.2
Add and .
Step 6.5.4.2
Subtract from both sides of the equation.
Step 6.5.4.3
Divide each term in by and simplify.
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Step 6.5.4.3.1
Divide each term in by .
Step 6.5.4.3.2
Simplify the left side.
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Step 6.5.4.3.2.1
Cancel the common factor of .
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Step 6.5.4.3.2.1.1
Cancel the common factor.
Step 6.5.4.3.2.1.2
Divide by .
Step 6.5.4.3.3
Simplify the right side.
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Step 6.5.4.3.3.1
Move the negative in front of the fraction.
Step 6.5.5
Solve for .
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Step 6.5.5.1
Multiply by .
Step 6.5.5.2
Move all terms containing to the left side of the equation.
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Step 6.5.5.2.1
Subtract from both sides of the equation.
Step 6.5.5.2.2
Subtract from .
Step 6.5.5.3
Subtract from both sides of the equation.
Step 6.5.5.4
Divide each term in by and simplify.
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Step 6.5.5.4.1
Divide each term in by .
Step 6.5.5.4.2
Simplify the left side.
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Step 6.5.5.4.2.1
Cancel the common factor of .
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Step 6.5.5.4.2.1.1
Cancel the common factor.
Step 6.5.5.4.2.1.2
Divide by .
Step 6.5.5.4.3
Simplify the right side.
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Step 6.5.5.4.3.1
Cancel the common factor of and .
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Step 6.5.5.4.3.1.1
Factor out of .
Step 6.5.5.4.3.1.2
Cancel the common factors.
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Step 6.5.5.4.3.1.2.1
Factor out of .
Step 6.5.5.4.3.1.2.2
Cancel the common factor.
Step 6.5.5.4.3.1.2.3
Rewrite the expression.
Step 6.5.6
Consolidate the solutions.
Step 6.6
Consolidate the solutions.
Step 7
Solve for .
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Step 7.1
Solve for .
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Step 7.1.1
Rewrite the equation as .
Step 7.1.2
Simplify .
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Step 7.1.2.1
Apply the distributive property.
Step 7.1.2.2
Multiply .
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Step 7.1.2.2.1
Multiply by .
Step 7.1.2.2.2
Multiply by .
Step 7.1.3
Subtract from both sides of the equation.
Step 7.1.4
Divide each term in by and simplify.
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Step 7.1.4.1
Divide each term in by .
Step 7.1.4.2
Simplify the left side.
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Step 7.1.4.2.1
Dividing two negative values results in a positive value.
Step 7.1.4.2.2
Divide by .
Step 7.1.4.3
Simplify the right side.
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Step 7.1.4.3.1
Simplify each term.
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Step 7.1.4.3.1.1
Move the negative one from the denominator of .
Step 7.1.4.3.1.2
Rewrite as .
Step 7.1.4.3.1.3
Multiply by .
Step 7.1.4.3.1.4
Dividing two negative values results in a positive value.
Step 7.1.4.3.1.5
Divide by .
Step 7.2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 7.3
The result consists of both the positive and negative portions of the .
Step 7.4
Solve for .
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Step 7.4.1
Solve for .
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Step 7.4.1.1
Rewrite the equation as .
Step 7.4.1.2
Move all terms not containing to the right side of the equation.
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Step 7.4.1.2.1
Add to both sides of the equation.
Step 7.4.1.2.2
Add and .
Step 7.4.2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 7.4.3
The result consists of both the positive and negative portions of the .
Step 7.4.4
Solve for .
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Step 7.4.4.1
Move all terms containing to the left side of the equation.
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Step 7.4.4.1.1
Subtract from both sides of the equation.
Step 7.4.4.1.2
Subtract from .
Step 7.4.4.2
Subtract from both sides of the equation.
Step 7.4.4.3
Divide each term in by and simplify.
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Step 7.4.4.3.1
Divide each term in by .
Step 7.4.4.3.2
Simplify the left side.
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Step 7.4.4.3.2.1
Cancel the common factor of .
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Step 7.4.4.3.2.1.1
Cancel the common factor.
Step 7.4.4.3.2.1.2
Divide by .
Step 7.4.4.3.3
Simplify the right side.
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Step 7.4.4.3.3.1
Cancel the common factor of and .
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Step 7.4.4.3.3.1.1
Factor out of .
Step 7.4.4.3.3.1.2
Cancel the common factors.
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Step 7.4.4.3.3.1.2.1
Factor out of .
Step 7.4.4.3.3.1.2.2
Cancel the common factor.
Step 7.4.4.3.3.1.2.3
Rewrite the expression.
Step 7.4.5
Solve for .
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Step 7.4.5.1
Multiply by .
Step 7.4.5.2
Move all terms containing to the left side of the equation.
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Step 7.4.5.2.1
Add to both sides of the equation.
Step 7.4.5.2.2
Add and .
Step 7.4.5.3
Subtract from both sides of the equation.
Step 7.4.5.4
Divide each term in by and simplify.
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Step 7.4.5.4.1
Divide each term in by .
Step 7.4.5.4.2
Simplify the left side.
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Step 7.4.5.4.2.1
Cancel the common factor of .
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Step 7.4.5.4.2.1.1
Cancel the common factor.
Step 7.4.5.4.2.1.2
Divide by .
Step 7.4.5.4.3
Simplify the right side.
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Step 7.4.5.4.3.1
Move the negative in front of the fraction.
Step 7.4.6
Consolidate the solutions.
Step 7.5
Solve for .
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Step 7.5.1
Solve for .
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Step 7.5.1.1
Rewrite the equation as .
Step 7.5.1.2
Simplify .
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Step 7.5.1.2.1
Apply the distributive property.
Step 7.5.1.2.2
Multiply by .
Step 7.5.1.3
Move all terms not containing to the right side of the equation.
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Step 7.5.1.3.1
Subtract from both sides of the equation.
Step 7.5.1.3.2
Subtract from .
Step 7.5.1.4
Divide each term in by and simplify.
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Step 7.5.1.4.1
Divide each term in by .
Step 7.5.1.4.2
Simplify the left side.
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Step 7.5.1.4.2.1
Dividing two negative values results in a positive value.
Step 7.5.1.4.2.2
Divide by .
Step 7.5.1.4.3
Simplify the right side.
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Step 7.5.1.4.3.1
Move the negative one from the denominator of .
Step 7.5.1.4.3.2
Rewrite as .
Step 7.5.2
Remove the absolute value term. This creates a on the right side of the equation because .
Step 7.5.3
The result consists of both the positive and negative portions of the .
Step 7.5.4
Solve for .
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Step 7.5.4.1
Move all terms containing to the left side of the equation.
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Step 7.5.4.1.1
Add to both sides of the equation.
Step 7.5.4.1.2
Add and .
Step 7.5.4.2
Subtract from both sides of the equation.
Step 7.5.4.3
Divide each term in by and simplify.
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Step 7.5.4.3.1
Divide each term in by .
Step 7.5.4.3.2
Simplify the left side.
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Step 7.5.4.3.2.1
Cancel the common factor of .
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Step 7.5.4.3.2.1.1
Cancel the common factor.
Step 7.5.4.3.2.1.2
Divide by .
Step 7.5.4.3.3
Simplify the right side.
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Step 7.5.4.3.3.1
Move the negative in front of the fraction.
Step 7.5.5
Solve for .
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Step 7.5.5.1
Move all terms containing to the left side of the equation.
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Step 7.5.5.1.1
Subtract from both sides of the equation.
Step 7.5.5.1.2
Combine the opposite terms in .
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Step 7.5.5.1.2.1
Subtract from .
Step 7.5.5.1.2.2
Add and .
Step 7.5.5.2
Since , there are no solutions.
No solution
No solution
Step 7.5.6
Consolidate the solutions.
Step 7.6
Consolidate the solutions.
Step 8
Consolidate the solutions.
Step 9
Exclude the solutions that do not make true.
Step 10
The result can be shown in multiple forms.
Exact Form:
Decimal Form:
Mixed Number Form: