MHB Solve the inequality and graph the solution on a real number line

[megacat8921]

(3x - 5)/(x - 5) > 4

How does one complete this problem?

 

[MarkFL]

We are given to solve:

$$\frac{3x-5}{x-5}>4$$

Now, one might be tempted to multiply through by $x-5$ to clear the denominator on the right side, as we would with an equation. But with inequalities, we have to be mindful of the sign of a multiplicative quantity, so our best strategy here is to subtract 4 from both sides:

$$\frac{3x-5}{x-5}-4>0$$

Now, you need to combine terms on the left, and then determine your critical numbers, which are found anywhere the numerator AND denominator is zero. Can you proceed?

 

[megacat8921]

Yes, thank you.