Solve for x |x+1|=|-x-9|

$| x + 1 | = | - x - 9 |$

Rewrite the equation as $| - x - 9 | = | x + 1 |$ .

$| - x - 9 | = | x + 1 |$

Rewrite the absolute value equation as four equations without absolute value bars.

$- x - 9 = x + 1$

$- x - 9 = - (x + 1)$

$- (- x - 9) = x + 1$

$- (- x - 9) = - (x + 1)$

After simplifying, there are only two unique equations to be solved.

$- x - 9 = x + 1$

$- x - 9 = - (x + 1)$

Solve $- x - 9 = x + 1$ for $x$ .

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

Subtract $x$ from both sides of the equation.

$- x - 9 - x = 1$

Subtract $x$ from $- x$ .

$- 2 x - 9 = 1$

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

Add $9$ to both sides of the equation.

$- 2 x = 1 + 9$

Add $1$ and $9$ .

$- 2 x = 10$

Divide each term in $- 2 x = 10$ by $- 2$ and simplify.

Divide each term in $- 2 x = 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

Divide $x$ by $1$ .

$x = \frac{10}{- 2}$

Simplify the right side.

Divide $10$ by $- 2$ .

$x = - 5$

Solve $- x - 9 = - (x + 1)$ for $x$ .

Simplify $- (x + 1)$ .

Rewrite.

$- x - 9 = 0 + 0 - (x + 1)$

Simplify by adding zeros.

$- x - 9 = - (x + 1)$

Apply the distributive property.

$- x - 9 = - x - 1 \cdot 1$

Multiply $- 1$ by $1$ .

$- x - 9 = - x - 1$

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

Add $x$ to both sides of the equation.

$- x - 9 + x = - 1$

Combine the opposite terms in $- x - 9 + x$ .

Add $- x$ and $x$ .

$0 - 9 = - 1$

Subtract $9$ from $0$ .

$- 9 = - 1$

Since $- 9 \neq - 1$ , there are no solutions.

No solution

List all of the solutions.

$x = - 5$

Solve for x |x+1|=|-x-9|

Related Questions

Support LCMGCF.com by disabling your adblocker.