MHT CET · Maths · Basic of Mathematics
If \(|3 x-2| \leq \frac{1}{2} \quad\) then \(x \in\)
- A \(\left[\frac{1}{2}, \frac{5}{6}\right]\)
- B \(\left(\frac{1}{2}, \frac{5}{6}\right]\)
- C \(\left[\frac{1}{2}, \frac{5}{6}\right)\)
- D \(\left(\frac{1}{2}, \frac{5}{6}\right)\)
Answer & Solution
Correct Answer
(A) \(\left[\frac{1}{2}, \frac{5}{6}\right]\)
Step-by-step Solution
Detailed explanation
We have \(|3 x-2| \leq \frac{1}{2}\)
\(\therefore \frac{-1}{2} \leq(3 x-2) \leq \frac{1}{2}\)
\(\therefore \frac{-1}{2} \leq 3 x-2 \quad\) and \(\quad 3 x-2 \leq \frac{1}{2}\)
\(\therefore \quad \frac{3}{2} \leq 3 x \quad\) and \(\quad 3 x \leq \frac{5}{2}\)
\(\quad \frac{1}{2} \leq x \quad\) and \(\quad x \leq \frac{5}{6}\)
\(\therefore x \in\left[\frac{1}{2}, \frac{5}{6}\right]\)
\(\therefore \frac{-1}{2} \leq(3 x-2) \leq \frac{1}{2}\)
\(\therefore \frac{-1}{2} \leq 3 x-2 \quad\) and \(\quad 3 x-2 \leq \frac{1}{2}\)
\(\therefore \quad \frac{3}{2} \leq 3 x \quad\) and \(\quad 3 x \leq \frac{5}{2}\)
\(\quad \frac{1}{2} \leq x \quad\) and \(\quad x \leq \frac{5}{6}\)
\(\therefore x \in\left[\frac{1}{2}, \frac{5}{6}\right]\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- Negation of the statement
"The payment will be made if and only if the work is finished in time." IsMHT CET 2023 Easy - A point moves along the arc of parabola \(y=2 x^2\). Its abscissa increases uniformly at the rate of 2 units \(/ \mathrm{sec}\). At the instant, the point is passing through \((1,2)\), its distance from origin is increasing at the rate ofMHT CET 2024 Hard
- The area bounded by the curve \(y^2=2 x+1\) and the line \(x-y=1\) isMHT CET 2022 Easy
- If \(P_1\) and \(P_2\) are perpendicular distances (in units) from point \((2,-1)\) to the pair of lines \(2 x^2-5 x y+2 y^2=0\), then the value of \(\mathrm{P}_1 \mathrm{P}_2\) isMHT CET 2024 Easy
- If \(\mathrm{f}(x)=\int \frac{x^2 \mathrm{~d} x}{\left(1+x^2\right)\left(1+\sqrt{1+x^2}\right)}\) and \(\mathrm{f}(0)=0\), then \(f(1)\) isMHT CET 2023 Hard
- If one of the diameters of the circle, given by the equation \(x^2+y^2-4 x+6 y-12=0\), is a chord of a circle, 'S', whose centre is at \((-3,2)\), then the length of radius of ' \(S\) ' is ______ units.MHT CET 2025 Medium
More PYQs from MHT CET
- The resistance of a conductivity cell of 0.1 M KCl solution is 120 ohm and conductivity is \(1.64 \times 10^{-4} \mathrm{~S} \mathrm{~cm}^{-1}\). What is the value of cell constant?MHT CET 2024 Easy
- If \(\mathrm{A}\left[\begin{array}{ll}2 & 1 \\ 7 & 4\end{array}\right]\) then \(\left(\mathrm{A}^2-5 \mathrm{~A}\right)^{-1}\) isMHT CET 2024 Medium
- The area of the region include between the parabolas \(y^2=8 x\) and \(\mathrm{x}^2=8 \mathrm{y}\), isMHT CET 2021 Easy
- A pair of hormones produced by kidneys isMHT CET 2016 Medium
- When both source and listener are approaching each other the observed frequency of sound is given by \(\left(V_L\right.\) and \(V_S\) is the velocity of listener and source respectively, \(\mathrm{n}_0=\) radiated frequency)MHT CET 2023 Medium
- A heterozygous tall pea plant was crossed with a dwarf pea plant. The progeny of cross shows _________ .MHT CET 2021 Easy