Find the Solution Set for the Nonlinear Inequality $\frac { 2 x + 1 } { x - 4 } \leq 5$

question 107

Multiple Choice

Find the solution set for the nonlinear inequality $\frac { 2 x + 1 } { x - 4 } \leq 5$ .

• A) \(( - \infty , - 4 ) \cup ( 7 , \infty )\)
• B) \(( - \infty , - 7 ) \cup [ 4 , \infty )\)
• C) \(( - \infty , 4 ) \cup [ 7 , \infty )\)
• D) \(( - \infty , 4 ]\)
• E) \(( - \infty , 7 )\)

---

Definitions:

Inequality

A mathematical statement that indicates the relationship of less than (<), greater than (>), less than or equal to (≤), or greater than or equal to (≥) between two expressions.

Critical Numbers

Values in the domain of a function where its derivative is zero or undefined, often marking potential maxima, minima, or inflection points.

Real Number Line

A visual representation of all real numbers arranged in order of value on a straight, horizontal line.

Inequality

A mathematical statement that shows the relationship between quantities that are not necessarily equal, using symbols like <, >, ≤, and ≥.