Solve for x |9-2x|=10+3x

$| 9 - 2 x | = 10 + 3 x$

Reorder $10$ and $3 x$ .

$| 9 - 2 x | = 3 x + 10$

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

$9 - 2 x = \pm (3 x + 10)$

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.

$9 - 2 x = 3 x + 10$

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

Subtract $3 x$ from both sides of the equation.

$9 - 2 x - 3 x = 10$

Subtract $3 x$ from $- 2 x$ .

$9 - 5 x = 10$

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

Subtract $9$ from both sides of the equation.

$- 5 x = 10 - 9$

Subtract $9$ from $10$ .

$- 5 x = 1$

Divide each term in $- 5 x = 1$ by $- 5$ and simplify.

Divide each term in $- 5 x = 1$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{1}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{1}{- 5}$

Divide $x$ by $1$ .

$x = \frac{1}{- 5}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{5}$

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

$9 - 2 x = - (3 x + 10)$

Simplify $- (3 x + 10)$ .

Rewrite.

$9 - 2 x = 0 + 0 - (3 x + 10)$

Simplify by adding zeros.

$9 - 2 x = - (3 x + 10)$

Apply the distributive property.

$9 - 2 x = - (3 x) - 1 \cdot 10$

Multiply.

Multiply $3$ by $- 1$ .

$9 - 2 x = - 3 x - 1 \cdot 10$

Multiply $- 1$ by $10$ .

$9 - 2 x = - 3 x - 10$

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

Add $3 x$ to both sides of the equation.

$9 - 2 x + 3 x = - 10$

Add $- 2 x$ and $3 x$ .

$9 + x = - 10$

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

Subtract $9$ from both sides of the equation.

$x = - 10 - 9$

Subtract $9$ from $- 10$ .

$x = - 19$

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

$x = - \frac{1}{5}, - 19$

Exclude the solutions that do not make $| 9 - 2 x | = 10 + 3 x$ true.

$x = - \frac{1}{5}$

The result can be shown in multiple forms.

Exact Form:

$x = - \frac{1}{5}$

Decimal Form:

$x = - 0.2$

Solve for x |9-2x|=10+3x

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