Find All Complex Solutions 3|5-x|+2=29

$3 | 5 - x | + 2 = 29$

Subtract $29$ from both sides of the equation.

$3 | 5 - x | + 2 - 29 = 0$

Subtract $29$ from $2$ .

$3 | 5 - x | - 27 = 0$

Factor $3$ out of $3 | 5 - x | - 27$ .

Factor $3$ out of $3 | 5 - x |$ .

$3 (| 5 - x |) - 27 = 0$

Factor $3$ out of $- 27$ .

$3 | 5 - x | + 3 \cdot - 9 = 0$

Factor $3$ out of $3 | 5 - x | + 3 \cdot - 9$ .

$3 (| 5 - x | - 9) = 0$

Divide each term in $3 (| 5 - x | - 9) = 0$ by $3$ and simplify.

Divide each term in $3 (| 5 - x | - 9) = 0$ by $3$ .

$\frac{3 (| 5 - x | - 9)}{3} = \frac{0}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 (| 5 - x | - 9)}{3} = \frac{0}{3}$

Divide $| 5 - x | - 9$ by $1$ .

$| 5 - x | - 9 = \frac{0}{3}$

Simplify the right side.

Divide $0$ by $3$ .

$| 5 - x | - 9 = 0$

Add $9$ to both sides of the equation.

$| 5 - x | = 9$

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

$5 - x = \pm 9$

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.

$5 - x = 9$

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

Subtract $5$ from both sides of the equation.

$- x = 9 - 5$

Subtract $5$ from $9$ .

$- x = 4$

Divide each term in $- x = 4$ by $- 1$ and simplify.

Divide each term in $- x = 4$ by $- 1$ .

$\frac{- x}{- 1} = \frac{4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{4}{- 1}$

Divide $x$ by $1$ .

$x = \frac{4}{- 1}$

Simplify the right side.

Divide $4$ by $- 1$ .

$x = - 4$

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

$5 - x = - 9$

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

Subtract $5$ from both sides of the equation.

$- x = - 9 - 5$

Subtract $5$ from $- 9$ .

$- x = - 14$

Divide each term in $- x = - 14$ by $- 1$ and simplify.

Divide each term in $- x = - 14$ by $- 1$ .

$\frac{- x}{- 1} = \frac{- 14}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{- 14}{- 1}$

Divide $x$ by $1$ .

$x = \frac{- 14}{- 1}$

Simplify the right side.

Divide $- 14$ by $- 1$ .

$x = 14$

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

$x = - 4, 14$

Find All Complex Solutions 3|5-x|+2=29

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