Questions: Solve the inequality. -4 / (-7 x - 4) > 0 (-4/7, ∞) (-∞, -7/4) (-∞, 4/7) (0, ∞)

Transcript text: Solve the inequality. \[ \frac{-4}{-7 x-4}>0 \] $\left(-\frac{4}{7}, \infty\right)$ $\left(-\infty,-\frac{7}{4}\right)$ $\left(-\infty, \frac{4}{7}\right)$ $(0, \infty)$

Solution

Solution Steps

Step 1: Simplify the Inequality

Given the inequality: \[ \frac{-4}{-7x - 4} > 0 \] We need to determine when the fraction is positive. A fraction is positive when both the numerator and the denominator have the same sign.

Step 2: Determine the Sign of the Denominator

The numerator $-4$ is always negative. Therefore, for the fraction to be positive, the denominator $-7x - 4$ must also be negative: \[ -7x - 4 < 0 \]

Step 3: Solve for $x$

Solve the inequality for $x$: \[ -7x - 4 < 0 \] Add 4 to both sides: \[ -7x < 4 \] Divide by $-7$ and reverse the inequality sign: \[ x > -\frac{4}{7} \]