Solution of 

\left | 3m-2\right |\geq 1 is 

  • Option 1)

    \left [ \frac{1}{3}, 1 \right ]

  • Option 2)

    \left ( \frac{1}{3}, 1 \right )

  • Option 3)

    \left ( \frac{1}{2}, 1 \right )

  • Option 4)

    \left ( -\infty ,\frac{1}{3} \right ]\cup \left [ 1,\infty \right )

 

Answers (1)
A Aadil

 

As learnt in concept

UNION OF SETS -

Let A and B be any two sets. The union of A and B is the set which consists of all the elements of A and all the elements of B, the common elements being taken only once. The symbol ‘∪’ is used to denote the union.

- wherein

Symbolically, we write A U B = {x: x ∈ A or x ∈ B}.

 

 \left | 3m-2 \right |\geqslant \left 1

So

3m-2\geqslant 1\: \Rightarrow m\geq 1\ or\: 3m-2\leqslant -1 \Rightarrow m \leq \frac{1}{3}

             

m\ \epsilon (-\infty,\frac{1}{3}]\cup [1, \infty)


Option 1)

\left [ \frac{1}{3}, 1 \right ]

This is incorrect option

Option 2)

\left ( \frac{1}{3}, 1 \right )

This is incorrect option

Option 3)

\left ( \frac{1}{2}, 1 \right )

This is incorrect option

Option 4)

\left ( -\infty ,\frac{1}{3} \right ]\cup \left [ 1,\infty \right )

This is correct option

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