The times taken by 25 people to complete a puzzle are shown draw a frequency polygon for the dtaa

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sanociahnoel

10.05.2023

Mathematics

A. X < 3.

Step-by-step explanation:

We have the equation, $3 + \frac{x-2}{x-3} \leq 4$

Adding -4 on both sides, we get,

$\frac{x-2}{x-3} -1 \leq 0$

i.e. $\frac{x-2-x+3}{x-3} \leq 0$

i.e. $\frac{1}{x-3} \leq 0$

So, we have the inequality $\frac{1}{x-3} \leq 0$ .

Its critical points are given by x-3 = 0 which implies x = 3.

Now, we will find the region among the two $( - \infty , 3 )$ and $( 3 , \infty )$ that satisfies the inequality $\frac{x-2}{x-3} -1 \leq 0$

Substitute x = 2 in the above inequality, we get -1 < 0, which is true. Again, substitute x=4 gives 1 < 0, which is false.

As x=4 lie in the region $( 3 , \infty )$ , it cannot be the solution of the given inequality.

So, the solution of the given inequality is the region $( - \infty , 3 )$ .i.e. x < 3.

Hence. option A is correct.

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