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Numerical Inequalities · Question 56 of 79

Question 56

HardOriginal question

Solve x−2x+3>0\frac{x - 2}{x + 3} > 0.

Options for question 56

Show the answer and explanation
CorrectNot quiteAnswer B

Correct answer: B

Explanation

  1. A fraction is positive when the top and bottom have the same sign. The signs change at x=2x = 2 and x=−3x = -3.

  2. Both positive: x>2x > 2. Both negative: x<−3x < -3. Neither end point is allowed: at 2 the fraction is 0, at −3-3 it is undefined.

Worth noting

Including −3-3 divides by zero, and including 2 gives 0, which is not >0> 0.

Concept
A rational inequation
Typical time
120 s
Your time
—
The rule this testsSolving inequations
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Ten questions from Numerical Inequalities, at your own pace.

Practise this chapter →

Ten questions from Numerical Inequalities, at your own pace.