JAMB Mathematics 2014 Paper

Concept:Solve the inequality by bringing all terms to one side and testing the sign of the resulting rational expression.Explanation:Start with$$\frac{x-5}{x+3} < -1$$Add $1$ to both sides to combine the terms:$$\frac{x-5}{x+3} + 1 < 0$$Write $1$ with the same denominator:$$\frac{x-5 + x+3}{x+3} < 0$$Simplify the numerator:$$\frac{2x - 2}{x+3} < 0$$Factor the numerator:$$\frac{2(x-1)}{x+3} < 0$$The critical values are $x = -3$ and $x = 1$.These values divide the number line into intervals.Test $x = 0$, which lies in the interval $-3 < x < 1$:$$\frac{2(0-1)}{0+3} = \frac{-2}{3} < 0$$This satisfies the inequality.For $x < -3$ or $x > 1$, the expression is positive, so it does not satisfy the inequality.Thus, the solution is the open interval from $-3$ to $1$.Answer:A. $-3 < x < 1$