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in Linear Inequations by (48.0k points)
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If x is an integer greater than -10, but less than 10 and |x – 2| < 3, then the values of x are

(a) –10, –9, –8, –7, –6, –5, –4, –3, –2, –1, 0, 1, 2, 3, 4

(b) 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10

(c) 0, 1, 2, 3, 4

(d) –1, 0, 1

1 Answer

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Best answer

Correct option is (c) 0, 1, 2, 3, 4

It is given that 

−10 < x < 10

That is 

∣x∣ < 10 ...(i)

Now 

∣x − 2∣ < 3

−3 < x − 2 < 3

−1 < x < 5 ...(ii)

Hence 

From (ii),

x \(\in\) (−1, 5) and 

From (i),

x \(\in\) (−10, 10)

Hence

x \(\in\) (−1, 5)

Now x is an integer.

Hence the set of integers falling in the above solution set is {0, 1, 2, 3, 4}.

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