Question

A student attempted to solve the inequality $\frac{x+4}{x-3}\le 0$by multiplying both sides of the inequality by $x-3$to get $x+4\le 0$. This led to a solution of $\{x\mid x\le -4\}$. Is the student correct? Explain.

Short answer

No, the student is not correct.

Step-by-step solution

Given information

The given inequality is $\frac{x+4}{x-3}\le 0$.

Determine whether the student is correct or not.

Multiplying both sides of inequality:

$\frac{x+4}{x-3}\le 0$

by $\left(x-3\right)$is not allowed when $x<3$since it swaps the $\le$symbol into$\ge$.

$x\in [-4,3)$

Write the conclusion

No student wasn't correct, correct solution is:$\{x\mid x\in [-4,3\left)\right\}$