KCET · Maths · Basic of Mathematics

Consider the following statements :
Statement(I) : The set of all solutions of the linear inequalities \(3 x+8 \lt 17\) and \(2 x+8 \geq 12\) are \(x \lt 3\) and \(x \geq 2\) respectively.
Statement(II) : The common set of solutions of linear inequalities \(3 x+8 \lt 17\) and \(2 x+8 \geq 12\) is \((2,3)\).
Which of the following is true?

A Statement (I) is true but statement (II) is false
B Statement (I) is false but statement (II) is true
C Both the statements are true
D Both the statements are false

Verified Solution

Answer & Solution

Correct Answer

(A) Statement (I) is true but statement (II) is false

Step-by-step Solution

Detailed explanation

\(\begin{aligned}
& 3 x+8 \lt 17 \Rightarrow 3 x \lt 9 \Rightarrow x \lt 3 \\
& 2 x+8 \geq 12 \Rightarrow 2 x \geq 4 \Rightarrow x \geq 2
\end{aligned}\)

Statement I is correct.
The common set of solution \(\Rightarrow\{2\}\)
\(\rightarrow\) Statement II is false

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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