Let’s consider scenarios where m>0 and m<0. Note that m cannot equal zero because then the denominator of the left side of the inequality would be zero: If m is positive, (m > 0), then:

(4 – m) / m >= 5

4 – m >= 5m

4 >= 6m

4 / 6 >= m

m <= 2/3 If m is negative, (m < 0), then you'll want to know, "for which values of m is the following statement true?" (4 - (-m)) / (-m) >= 5

(4 + m) / (-m) >= 5

But notice how, (when m is negative), the left hand side of the inequality will always have a positive numerator and a negative denominator, which means that the left hand side of the inequality is always negative when m is negative. In other words, the left hand side of the inequality cannot be greater than or equal to 5 if m is negative; therefore, m cannot be negative.

In other words, for this inequality: (4 – m) / m >= 5,

0 < m <= 2/3.

4-.66 /.66>=5

3.34/.66>=5

5.06>=5

CORRECT!!!