Chapter 4.4, Problem 78AYU

To determine

To explain:

Student has solved the inequality equation $\frac{x+4}{x-3}\le 0$ and its solution is $\left\{x|x\le -4\right\}$ , this solution is correct or not

Answer to Problem 78AYU

No. A student is not correct.

Explanation of Solution

Problem states that:

The result of $\frac{x+4}{x-3}\le 0$ is $x+4\le 0$ . This result is done by multiplying $x-3$ on the both sides of the inequality equation.

So, the solution resulted by student $\left\{x|x\le -4\right\}$ is not correct because the multiplication on both sides of the inequality equation by the term $x-3$ is not possible. As it depends on whether the value of $x>3OR\text{}x<3$ .

If $x<3$ then $x-3<0$ is used to multiply on both sides of the equation but there is need to switch the inequality sign.

So, in general switching of the inequality sign for any algebraic operations is wrong that’s why the given solution represented by student is wrong.