Chapter 4: Q. 84 (page 243)

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

Short Answer

Expert verified

No, the student is not correct.

Step by step solution

Given information

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

Determine whether the student is correct or not.

Multiplying both sides of inequality:

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

by $(x - 3)$ is not allowed when $x < 3$ since it swaps the $\leq$ symbol into $\geq$ .

$x \in [- 4, 3)$

Write the conclusion

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

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

Short Answer

Step by step solution

Given information

Determine whether the student is correct or not.

Write the conclusion

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

Short Answer

Step by step solution

Given information

Determine whether the student is correct or not.

Write the conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Geometry

Pure Maths

Probability and Statistics

Logic and Functions

Calculus

Study anywhere. Anytime. Across all devices.

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