Solve the Inequality for x |2x|<14

$| 2 x | < 14$

Write $| 2 x | < 14$ as a piecewise.

To find the interval for the first piece, find where the inside of the absolute value is non-negative.

$2 x \geq 0$

Divide each term in $2 x \geq 0$ by $2$ and simplify.

Divide each term in $2 x \geq 0$ by $2$ .

$\frac{2 x}{2} \geq \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} \geq \frac{0}{2}$

Divide $x$ by $1$ .

$x \geq \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x \geq 0$

In the piece where $2 x$ is non-negative, remove the absolute value.

$2 x < 14$

To find the interval for the second piece, find where the inside of the absolute value is negative.

$2 x < 0$

Divide each term in $2 x < 0$ by $2$ and simplify.

Divide each term in $2 x < 0$ by $2$ .

$\frac{2 x}{2} < \frac{0}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{0}{2}$

Divide $x$ by $1$ .

$x < \frac{0}{2}$

Simplify the right side.

Divide $0$ by $2$ .

$x < 0$

In the piece where $2 x$ is negative, remove the absolute value and multiply by $- 1$ .

$- 2 x < 14$

Write as a piecewise.

${\begin{cases} 2 x < 14 & x \geq 0 \\ - 2 x < 14 & x < 0 \end{cases}$

Solve $2 x < 14$ when $x \geq 0$ .

Divide each term in $2 x < 14$ by $2$ and simplify.

Divide each term in $2 x < 14$ by $2$ .

$\frac{2 x}{2} < \frac{14}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} < \frac{14}{2}$

Divide $x$ by $1$ .

$x < \frac{14}{2}$

Simplify the right side.

Divide $14$ by $2$ .

$x < 7$

Find the intersection of $x < 7$ and $x \geq 0$ .

$0 \leq x < 7$

Solve $- 2 x < 14$ when $x < 0$ .

Divide each term in $- 2 x < 14$ by $- 2$ and simplify.

Divide each term in $- 2 x < 14$ by $- 2$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- 2 x}{- 2} > \frac{14}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} > \frac{14}{- 2}$

Divide $x$ by $1$ .

$x > \frac{14}{- 2}$

Simplify the right side.

Divide $14$ by $- 2$ .

$x > - 7$

Find the intersection of $x > - 7$ and $x < 0$ .

$- 7 < x < 0$

Find the union of the solutions.

$- 7 < x < 7$

The result can be shown in multiple forms.

Inequality Form:

$- 7 < x < 7$

Interval Notation:

$(- 7, 7)$

Solve the Inequality for x |2x|<14

Related Questions

Support LCMGCF.com by disabling your adblocker.