Mathematics 2014 JAMB Past Questions - Question 17: What is the solution of x-5/x+3

Correct Answer

B

Explanation

To solve the inequality (x - 5)/(x + 3) < -1, we can follow these steps:Step 1: Find the values of x that make the denominator (x + 3) equal to zero. In this case, x = -3 would make the denominator zero.Step 2: Determine the intervals on the number line based on the critical points found in Step 1. We have one critical point at x = -3, so we can divide the number line into two intervals: (-∞, -3) and (-3, +∞).Step 3: Test a value from each interval to determine the sign of the expression (x - 5)/(x + 3).For the interval (-∞, -3):Let's choose x = -4 as a test value. Plugging it into the expression, we get:((-4) - 5)/((-4) + 3) = (-9)/(-1) = 9Since 9 is positive, the expression is positive in this interval.For the interval (-3, +∞):Let's choose x = 0 as a test value. Plugging it into the expression, we get:((0) - 5)/((0) + 3) = (-5)/(3)Since -5/3 is negative, the expression is negative in this interval.Step 4: Analyze the signs of the expression in each interval to determine the solution to the inequality.In the interval (-∞, -3), the expression is positive, but we are looking for values where the expression is less than -1. Therefore, this interval does not satisfy the inequality.In the interval (-3, +∞), the expression is negative, which satisfies the inequality.Therefore, the solution to the inequality (x - 5)/(x + 3) < -1 is x ∈ (-3, +∞).