For the inequality system $x + y l e 6$ , $xg e 1$ , $y g e 2$ , what is the largest possible value of $x$ ?

medium MCQ 3 marks Class 11 · Mathematics · Linear Inequalities

Answer

The correct answer is 4 — Hence the maximum value of $x$ is $4$ .

Step-by-step solution

From $x + y l e 6$ and $y g e 2$ , deduce $x + 2 l e 6 R i g h t a r r o w x l e 4$ .
Given $xg e 1$ , the allowable values of $x$ are $1 l e x l e 4$ .
Hence the maximum value of $x$ is $4$ .

Common mistake: Overlooking the lower bound on

y

, leading to an incorrect maximum of

5

Concept tested: Extreme values in inequality systems