Exercise 2.8-Additional Questions - Chapter 2 Basic Algebra 11th Maths Guide Samacheer Kalvi Solutions - SaraNextGen [2024-2025]

Updated On May 15, 2024

By SaraNextGen

Additional Questions
Question 1.
Solve $\frac{x-2}{x+4} \geq \frac{5}{x+3}$
Solution:
$
\begin{aligned}
& \frac{(x-2)}{(x+4)}-\frac{5}{x+3} \geq 0 \\
& \frac{(x-2)(x+3)-5(x+4)}{(x+4)(x+3)} \geq 0 \\
& \frac{x^2+x-6-5 x-20}{(x+4)(x+3)} \geq 0 \\
\text { (i.e.,) } \quad & \frac{x^2-4 x-26}{(x+4)(x+3)} \geq 0 \\
& x+4=0 \Rightarrow x=-4 ; x+3=0 \Rightarrow x=-3
\end{aligned}
$
Plotting the points $-4,-3$ on number line and taking limits $(-\infty,-4),(-4,-3),(-3, \infty)$

$\text { The solution for the inequality } \frac{x-2}{x+4} \geq \frac{5}{x+3} \text { are the intervals }(-\infty,-4) \text { and }(-4,-3)$