KCET · Maths · Basic of Mathematics
If \( |3 x-5| \leq 2 \) then
- A \( 1 \leq x \leq \frac{7}{3} \)
- B \( -1 \leq x \leq \frac{9}{3} \)
- C \( -1 \leq x \leq \frac{7}{3} \)
- D \( 1 \leq x \leq \frac{9}{3} \)
Answer & Solution
Correct Answer
(A) \( 1 \leq x \leq \frac{7}{3} \)
Step-by-step Solution
Detailed explanation
(A)
\[
\begin{array}{l}
|3 x-5| \leq 2 \\
\Rightarrow-2 \leq 3 x-5 \leq 2 \\
\Rightarrow 3 \leq 3 x \leq 7 \\
\Rightarrow 1 \leq x \leq \frac{7}{3}
\end{array}
\]
\[
\begin{array}{l}
|3 x-5| \leq 2 \\
\Rightarrow-2 \leq 3 x-5 \leq 2 \\
\Rightarrow 3 \leq 3 x \leq 7 \\
\Rightarrow 1 \leq x \leq \frac{7}{3}
\end{array}
\]
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