# Solve for x |x|+x=2 Subtract from both sides of the equation.
Reorder and .
Remove the absolute value term. This creates a on the right side of the equation because .
Set up the positive portion of the solution.
Solve the first equation for .
Move all terms containing to the left side of the equation.
Add to both sides of the equation.
Divide each term by and simplify.
Divide each term in by .
Cancel the common factor of .
Cancel the common factor.
Divide by .
Divide by .
Set up the negative portion of the solution.
Solve the second equation for .
Simplify .
Apply the distributive property.
Multiply .
Multiply by .
Multiply by .
Multiply by .
Move all terms containing to the left side of the equation.
Subtract from both sides of the equation.
Subtract from .
Since , there are no solutions.
No solution
No solution
The solution to the equation includes both the positive and negative portions of the solution.
Verify each of the solutions by substituting them into and solving.
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