Simplify -2>4/4+5/(4x)

$- 2 > \frac{4}{4} + \frac{5}{4 x}$

Rewrite so $x$ is on the left side of the inequality.

$\frac{4}{4} + \frac{5}{4 x} < - 2$

Divide $4$ by $4$ .

$1 + \frac{5}{4 x} < - 2$

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

Subtract $1$ from both sides of the inequality.

$\frac{5}{4 x} < - 2 - 1$

Subtract $1$ from $- 2$ .

$\frac{5}{4 x} < - 3$

Multiply both sides by $4 x$ .

$\frac{5}{4 x} (4 x) = - 3 (4 x)$

Simplify.

Simplify the left side.

Simplify $\frac{5}{4 x} (4 x)$ .

Rewrite using the commutative property of multiplication.

$4 \frac{5}{4 x} x = - 3 (4 x)$

Cancel the common factor of $4$ .

Factor $4$ out of $4 x$ .

$4 \frac{5}{4 (x)} x = - 3 (4 x)$

Cancel the common factor.

$4 \frac{5}{4 x} x = - 3 (4 x)$

Rewrite the expression.

$\frac{5}{x} x = - 3 (4 x)$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{5}{x} x = - 3 (4 x)$

Rewrite the expression.

$5 = - 3 (4 x)$

Simplify the right side.

Multiply $4$ by $- 3$ .

$5 = - 12 x$

Solve for $x$ .

Rewrite the equation as $- 12 x = 5$ .

$- 12 x = 5$

Divide each term in $- 12 x = 5$ by $- 12$ and simplify.

Divide each term in $- 12 x = 5$ by $- 12$ .

$\frac{- 12 x}{- 12} = \frac{5}{- 12}$

Simplify the left side.

Cancel the common factor of $- 12$ .

Cancel the common factor.

$\frac{- 12 x}{- 12} = \frac{5}{- 12}$

Divide $x$ by $1$ .

$x = \frac{5}{- 12}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{12}$

Find the domain of $- 3 - \frac{5}{4 x}$ .

Set the denominator in $\frac{5}{4 x}$ equal to $0$ to find where the expression is undefined.

$4 x = 0$

Divide each term in $4 x = 0$ by $4$ and simplify.

Divide each term in $4 x = 0$ by $4$ .

$\frac{4 x}{4} = \frac{0}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{0}{4}$

Divide $x$ by $1$ .

$x = \frac{0}{4}$

Simplify the right side.

Divide $0$ by $4$ .

$x = 0$

The domain is all values of $x$ that make the expression defined.

$(- \infty, 0) \cup (0, \infty)$

Use each root to create test intervals.

$x < - \frac{5}{12}$

$- \frac{5}{12} < x < 0$

$x > 0$

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

Test a value on the interval $x < - \frac{5}{12}$ to see if it makes the inequality true.

Choose a value on the interval $x < - \frac{5}{12}$ and see if this value makes the original inequality true.

$x = - 3$

Replace $x$ with $- 3$ in the original inequality.

$- 2 > \frac{4}{4} + \frac{5}{4 (- 3)}$

The left side $- 2$ is not greater than the right side $0.58\overline{3}$ , which means that the given statement is false.

False

Test a value on the interval $- \frac{5}{12} < x < 0$ to see if it makes the inequality true.

Choose a value on the interval $- \frac{5}{12} < x < 0$ and see if this value makes the original inequality true.

$x = - 0.21$

Replace $x$ with $- 0.21$ in the original inequality.

$- 2 > \frac{4}{4} + \frac{5}{4 (- 0.21)}$

The left side $- 2$ is greater than the right side $- 4.\overline{952380}$ , which means that the given statement is always true.

True

Test a value on the interval $x > 0$ to see if it makes the inequality true.

Choose a value on the interval $x > 0$ and see if this value makes the original inequality true.

$x = 2$

Replace $x$ with $2$ in the original inequality.

$- 2 > \frac{4}{4} + \frac{5}{4 (2)}$

The left side $- 2$ is not greater than the right side $1.625$ , which means that the given statement is false.

False

Compare the intervals to determine which ones satisfy the original inequality.

$x < - \frac{5}{12}$ False

$- \frac{5}{12} < x < 0$ True

$x > 0$ False

$x < - \frac{5}{12}$ False

$- \frac{5}{12} < x < 0$ True

$x > 0$ False

The solution consists of all of the true intervals.

$- \frac{5}{12} < x < 0$

The result can be shown in multiple forms.

Inequality Form:

$- \frac{5}{12} < x < 0$

Interval Notation:

$(- \frac{5}{12}, 0)$

Simplify -2>4/4+5/(4x)

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