What is the solution set for the inequality (2x - 5)/(x - 1) ≤ 1?

What is the solution set for the inequality (2x - 5)/(x - 1) ≤ 1?

• A. (1, 4)
• B. (1, 4]
• C. [1, 4]
• D. (4, ∞)

Answer: (B)

To solve the inequality \((2x - 5)/(x - 1) ≤ 1\), we start by manipulating the inequality to isolate terms on one side. First, subtract 1 from both sides: \[ \frac{2x - 5}{x - 1} - 1 ≤ 0 \] This can be rewritten with a common denominator: \[ \frac{2x - 5 - (x - 1)}{x - 1} ≤ 0 \] Simplifying the numerator gives: \[ \frac{2x - 5 - x + 1}{x - 1} ≤ 0 \] \[ \frac{x - 4}{x - 1} ≤ 0 \] Next, we find the critical points of the inequality by setting the numerator and denominator to zero: 1. The numerator \(x - 4 = 0\) gives us \(x = 4\). 2. The denominator \(x - 1 = 0\) gives \(x = 1\). These points are important because they help us determine the sign of the expression \(\frac{x - 4}{x -

To solve the inequality ((2x - 5)/(x - 1) ≤ 1), we start by manipulating the inequality to isolate terms on one side.

First, subtract 1 from both sides:

[

\frac{2x - 5}{x - 1} - 1 ≤ 0

]

This can be rewritten with a common denominator:

[

\frac{2x - 5 - (x - 1)}{x - 1} ≤ 0

]

Simplifying the numerator gives:

[

\frac{2x - 5 - x + 1}{x - 1} ≤ 0

]

[

\frac{x - 4}{x - 1} ≤ 0

]

Next, we find the critical points of the inequality by setting the numerator and denominator to zero:

1. The numerator (x - 4 = 0) gives us (x = 4).

2. The denominator (x - 1 = 0) gives (x = 1).

These points are important because they help us determine the sign of the expression (\frac{x - 4}{x -