Solve for x |20x|=|4x+16|

$| 20 x | = | 4 x + 16 |$

Rewrite the equation as $| 4 x + 16 | = | 20 x |$ .

$| 4 x + 16 | = | 20 x |$

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

$4 x + 16 = 20 x$

$4 x + 16 = - 1 \cdot (20 x)$

$- (4 x + 16) = 20 x$

$- (4 x + 16) = - 1 \cdot (20 x)$

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

$4 x + 16 = 20 x$

$4 x + 16 = - 1 \cdot (20 x)$

Solve $4 x + 16 = 20 x$ for $x$ .

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

Subtract $20 x$ from both sides of the equation.

$4 x + 16 - 20 x = 0$

Subtract $20 x$ from $4 x$ .

$- 16 x + 16 = 0$

Subtract $16$ from both sides of the equation.

$- 16 x = - 16$

Divide each term in $- 16 x = - 16$ by $- 16$ and simplify.

Divide each term in $- 16 x = - 16$ by $- 16$ .

$\frac{- 16 x}{- 16} = \frac{- 16}{- 16}$

Simplify the left side.

Cancel the common factor of $- 16$ .

Cancel the common factor.

$\frac{- 16 x}{- 16} = \frac{- 16}{- 16}$

Divide $x$ by $1$ .

$x = \frac{- 16}{- 16}$

Simplify the right side.

Divide $- 16$ by $- 16$ .

$x = 1$

Solve $4 x + 16 = - 1 \cdot (20 x)$ for $x$ .

Multiply $20$ by $- 1$ .

$4 x + 16 = - 20 x$

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

Add $20 x$ to both sides of the equation.

$4 x + 16 + 20 x = 0$

Add $4 x$ and $20 x$ .

$24 x + 16 = 0$

Subtract $16$ from both sides of the equation.

$24 x = - 16$

Divide each term in $24 x = - 16$ by $24$ and simplify.

Divide each term in $24 x = - 16$ by $24$ .

$\frac{24 x}{24} = \frac{- 16}{24}$

Simplify the left side.

Cancel the common factor of $24$ .

Cancel the common factor.

$\frac{24 x}{24} = \frac{- 16}{24}$

Divide $x$ by $1$ .

$x = \frac{- 16}{24}$

Simplify the right side.

Cancel the common factor of $- 16$ and $24$ .

Factor $8$ out of $- 16$ .

$x = \frac{8 (- 2)}{24}$

Cancel the common factors.

Factor $8$ out of $24$ .

$x = \frac{8 \cdot - 2}{8 \cdot 3}$

Cancel the common factor.

$x = \frac{8 \cdot - 2}{8 \cdot 3}$

Rewrite the expression.

$x = \frac{- 2}{3}$

Move the negative in front of the fraction.

$x = - \frac{2}{3}$

List all of the solutions.

$x = 1, - \frac{2}{3}$

The result can be shown in multiple forms.

Exact Form:

$x = 1, - \frac{2}{3}$

Decimal Form:

$x = 1, - 0.\overline{6}$

Solve for x |20x|=|4x+16|

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