Question

which of the following is a solution to the inequality below?
-85 ≥ \frac{100}{v} - 4

v = -2

v = -4

v = -1

v = -5

Explanation:

Step1: Analyze the inequality

We have the inequality \(-85 \geq \frac{100}{v}-4\). First, we add 4 to both sides to isolate the fraction.
\(-85 + 4\geq\frac{100}{v}\)
\(-81\geq\frac{100}{v}\)

Step2: Test each value of \(v\)

• For \(v = - 2\):

Substitute \(v=-2\) into \(\frac{100}{v}\), we get \(\frac{100}{-2}=-50\). Now check if \(-81\geq - 50\). Since \(-81<-50\), \(v = - 2\) is not a solution.

• For \(v=-4\):

Substitute \(v = - 4\) into \(\frac{100}{v}\), we get \(\frac{100}{-4}=-25\). Now check if \(-81\geq - 25\). Since \(-81 < - 25\), \(v=-4\) is not a solution.

• For \(v=-1\):

Substitute \(v=-1\) into \(\frac{100}{v}\), we get \(\frac{100}{-1}=-100\). Now check if \(-81\geq - 100\). Since \(-81>-100\), \(v = - 1\) is a solution.

• For \(v=-5\):

Substitute \(v=-5\) into \(\frac{100}{v}\), we get \(\frac{100}{-5}=-20\). Now check if \(-81\geq - 20\). Since \(-81 < - 20\), \(v=-5\) is not a solution.

Answer:

\(v=-1\) (the option with \(v = - 1\))