Find All Complex Solutions |7x+21|=14x

$| 7 x + 21 | = 14 x$

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

$7 x + 21 = \pm 14 x$

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.

$7 x + 21 = 14 x$

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

Subtract $14 x$ from both sides of the equation.

$7 x + 21 - 14 x = 0$

Subtract $14 x$ from $7 x$ .

$- 7 x + 21 = 0$

Subtract $21$ from both sides of the equation.

$- 7 x = - 21$

Divide each term in $- 7 x = - 21$ by $- 7$ and simplify.

Divide each term in $- 7 x = - 21$ by $- 7$ .

$\frac{- 7 x}{- 7} = \frac{- 21}{- 7}$

Simplify the left side.

Cancel the common factor of $- 7$ .

Cancel the common factor.

$\frac{- 7 x}{- 7} = \frac{- 21}{- 7}$

Divide $x$ by $1$ .

$x = \frac{- 21}{- 7}$

Simplify the right side.

Divide $- 21$ by $- 7$ .

$x = 3$

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

$7 x + 21 = - 14 x$

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

Add $14 x$ to both sides of the equation.

$7 x + 21 + 14 x = 0$

Add $7 x$ and $14 x$ .

$21 x + 21 = 0$

Subtract $21$ from both sides of the equation.

$21 x = - 21$

Divide each term in $21 x = - 21$ by $21$ and simplify.

Divide each term in $21 x = - 21$ by $21$ .

$\frac{21 x}{21} = \frac{- 21}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 x}{21} = \frac{- 21}{21}$

Divide $x$ by $1$ .

$x = \frac{- 21}{21}$

Simplify the right side.

Divide $- 21$ by $21$ .

$x = - 1$

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

$x = 3, - 1$

Exclude the solutions that do not make $| 7 x + 21 | = 14 x$ true.

$x = 3$

Find All Complex Solutions |7x+21|=14x

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