To find the range of values of m which satisfy the inequality (m - 3)(m - 4) < 0, we can start by finding the critical points of the inequality, which are the values of m that make the expression equal to zero. These critical points are m = 3 and m = 4.

Next, we can divide the number line into three intervals based on these critical points: m < 3, 3 < m < 4, and m > 4. We can then test a value from each interval to see if it satisfies the inequality.

For m < 3, let's test m = 2. Substituting this value into the inequality gives us:

(2 - 3)(2 - 4) < 0

(-1)(-2) < 0

2 < 0

This is false, so the interval m < 3 does not satisfy the inequality.

For 3 < m < 4, let's test m = 3.5. Substituting this value into the inequality gives us:

(3.5 - 3)(3.5 - 4) < 0

(0.5)(-0.5) < 0

-0.25 < 0

This is true, so the interval 3 < m < 4 satisfies the inequality.

For m > 4, let's test m = 5. Substituting this value into the inequality gives us:

(5 - 3)(5 - 4) < 0

(2)(1) < 0

2 < 0

This is false, so the interval m > 4 does not satisfy the inequality.

Therefore, the range of values of m which satisfy the inequality (m - 3)(m - 4) < 0 is 3 < m < 4.