Q61 / 180 · KCET 2019 · Mathematics

If \( |3 x-5| \leq 2 \) then

  • Correct answer
    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
    \( 1 \leq x \leq \frac{9}{3} \)

Solution

(A)
\[ \begin{array}{l} |3 x-5| \leq 2 \\ \Rightarrow-2 \leq 3 x-5 \leq 2 \\ \Rightarrow 3 \leq 3 x \leq 7 \\ \Rightarrow 1 \leq x \leq \frac{7}{3} \end{array} \]

Hence, the correct answer is option: 'A'.

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