Answer: Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).
Step-by-step explanation: To find the range of values of x for which (3x-7)(x-5) ≥x+5, we first need to find the values of x for which the inequality is satisfied. We can do this by setting each factor equal to 0 and solving for x.
Setting (3x-7) equal to 0 gives us x=7/3. Setting (x-5) equal to 0 gives us x=5.
Next, we need to consider the signs of the factors. If both factors are positive or both are negative, the inequality will be satisfied. If one factor is positive and the other is negative, the inequality will not be satisfied.
For x<5, both factors are negative, so the inequality is satisfied. For x>5, both factors are positive, so the inequality is satisfied.
Therefore, the range of values of x for which (3x-7)(x-5) ≥x+5 is x<5 or x>5, or x∈(-∞,5)∪(5,∞).