Find All Complex Solutions |x+4|=x-1

$| x + 4 | = x - 1$

Remove the absolute value term. This creates a $\pm$ on the right side of the equation because $| x | = \pm x$ .

$x + 4 = \pm (x - 1)$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x + 4 = x - 1$

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

$x + 4 - x = - 1$

Combine the opposite terms in $x + 4 - x$ .

Subtract $x$ from $x$ .

$0 + 4 = - 1$

Add $0$ and $4$ .

$4 = - 1$

Since $4 \neq - 1$ , there are no solutions.

No solution

Next, use the negative value of the $\pm$ to find the second solution.

$x + 4 = - (x - 1)$

Simplify $- (x - 1)$ .

Rewrite.

$x + 4 = 0 + 0 - (x - 1)$

Simplify by adding zeros.

$x + 4 = - (x - 1)$

Apply the distributive property.

$x + 4 = - x - - 1$

Multiply $- 1$ by $- 1$ .

$x + 4 = - x + 1$

Move all terms containing $x$ to the left side of the equation.

Add $x$ to both sides of the equation.

$x + 4 + x = 1$

Add $x$ and $x$ .

$2 x + 4 = 1$

Move all terms not containing $x$ to the right side of the equation.

Subtract $4$ from both sides of the equation.

$2 x = 1 - 4$

Subtract $4$ from $1$ .

$2 x = - 3$

Divide each term in $2 x = - 3$ by $2$ and simplify.

Divide each term in $2 x = - 3$ by $2$ .

$\frac{2 x}{2} = \frac{- 3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 3}{2}$

Divide $x$ by $1$ .

$x = \frac{- 3}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{3}{2}$

The complete solution is the result of both the positive and negative portions of the solution.

$x =$

Find All Complex Solutions |x+4|=x-1

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