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

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

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Solution Steps

Step 1: Simplify the Inequality

Given the inequality: −4−7x−4>0 \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 −4-4 is always negative. Therefore, for the fraction to be positive, the denominator −7x−4-7x - 4 must also be negative: −7x−4<0 -7x - 4 < 0

Step 3: Solve for xx

Solve the inequality for xx: −7x−4<0 -7x - 4 < 0 Add 4 to both sides: −7x<4 -7x < 4 Divide by −7-7 and reverse the inequality sign: x>−47 x > -\frac{4}{7}

Final Answer

The solution to the inequality is: x>−47 x > -\frac{4}{7} This corresponds to the interval (−47,∞)\left( -\frac{4}{7}, \infty \right).

The correct answer is the third option.

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