Algebra Examples

$\frac{- 5}{- 4 x - 3} > 0$

Step 1

Solve $x > - \frac{3}{4}$ .

Tap for more steps...

Step 1.1

Find all the values where the expression switches from negative to positive by setting each factor equal to $0$ and solving.

$- 5 = 0$

$- 4 x - 3 = 0$

Step 1.2

Since $- 5 \neq 0$ , there are no solutions.

No solution

Step 1.3

Add $3$ to both sides of the equation.

$- 4 x = 3$

Step 1.4

Divide each term in $- 4 x = 3$ by $- 4$ and simplify.

Tap for more steps...

Step 1.4.1

Divide each term in $- 4 x = 3$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Step 1.4.2

Simplify the left side.

Tap for more steps...

Step 1.4.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 1.4.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Step 1.4.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{- 4}$

Step 1.4.3

Simplify the right side.

Tap for more steps...

Step 1.4.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

Step 1.5

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

Tap for more steps...

Step 1.5.1

Set the denominator in $\frac{- 5}{- 4 x - 3}$ equal to $0$ to find where the expression is undefined.

$- 4 x - 3 = 0$

Step 1.5.2

Solve for $x$ .

Tap for more steps...

Step 1.5.2.1

Add $3$ to both sides of the equation.

$- 4 x = 3$

Step 1.5.2.2

Divide each term in $- 4 x = 3$ by $- 4$ and simplify.

Tap for more steps...

Step 1.5.2.2.1

Divide each term in $- 4 x = 3$ by $- 4$ .

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Step 1.5.2.2.2

Simplify the left side.

Tap for more steps...

Step 1.5.2.2.2.1

Cancel the common factor of $- 4$ .

Tap for more steps...

Step 1.5.2.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{3}{- 4}$

Step 1.5.2.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{3}{- 4}$

Step 1.5.2.2.3

Simplify the right side.

Tap for more steps...

Step 1.5.2.2.3.1

Move the negative in front of the fraction.

$x = - \frac{3}{4}$

Step 1.5.3

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

$(- \infty, - \frac{3}{4}) \cup (- \frac{3}{4}, \infty)$

Step 1.6

The solution consists of all of the true intervals.

$x > - \frac{3}{4}$

Step 2

Use the inequality $x > - \frac{3}{4}$ to build the set notation.

${x | x > - \frac{3}{4}}$

Step 3