Solve for x 10+|9+4x|=11

$10 + | 9 + 4 x | = 11$

Step 1

Move all terms not containing $| 9 + 4 x |$ to the right side of the equation.

Subtract $10$ from both sides of the equation.

$| 9 + 4 x | = 11 - 10$

Subtract $10$ from $11$ .

$| 9 + 4 x | = 1$

Step 2

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

$9 + 4 x = \pm 1$

Step 3

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.

$9 + 4 x = 1$

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

Subtract $9$ from both sides of the equation.

$4 x = 1 - 9$

Subtract $9$ from $1$ .

$4 x = - 8$

Divide each term in $4 x = - 8$ by $4$ and simplify.

Divide each term in $4 x = - 8$ by $4$ .

$\frac{4 x}{4} = \frac{- 8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 8}{4}$

Divide $x$ by $1$ .

$x = \frac{- 8}{4}$

Simplify the right side.

Divide $- 8$ by $4$ .

$x = - 2$

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

$9 + 4 x = - 1$

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

Subtract $9$ from both sides of the equation.

$4 x = - 1 - 9$

Subtract $9$ from $- 1$ .

$4 x = - 10$

Divide each term in $4 x = - 10$ by $4$ and simplify.

Divide each term in $4 x = - 10$ by $4$ .

$\frac{4 x}{4} = \frac{- 10}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 10}{4}$

Divide $x$ by $1$ .

$x = \frac{- 10}{4}$

Simplify the right side.

Cancel the common factor of $- 10$ and $4$ .

Factor $2$ out of $- 10$ .

$x = \frac{2 (- 5)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot - 5}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot - 5}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{- 5}{2}$

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

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

$x = - 2, - \frac{5}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = - 2, - \frac{5}{2}$

Decimal Form:

$x = - 2, - 2.5$

Mixed Number Form:

$x = - 2, - 2 \frac{1}{2}$

Solve for x 10+|9+4x|=11

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