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Inequalities Involving Modulus Function

If x satisfie...

Question

If $x$ satisfies $| x - 1 | + | x - 2 | + | x - 3 | \geq 6$ , then

A

0 \leq x \leq 4

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B

x \leq - 2

or

x \geq 4

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C

x \leq 0

or

x \geq 4

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D

None of these

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Solution

The correct option is C $x \leq 0$ or $x \geq 4$
Let $| x - 1 | + | x - 2 | + | x - 3 | < 6$
or, $| (x - 1) + (x - 2) + (x - 3) | < | x - 1 | + | x - 2 | + | x - 3 | < 6$
or, $| 3 x - 6 | < 6$
or, $| x - 2 | < 2$
or, $- 2 < x - 2 < 2$
or, $0 < x < 4$
Therefore, for $| x - 1 | + | x - 2 | + | x - 3 | \geq 6, x \leq 0$ or $x \geq 4$

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Similar questions

x

| x - 1 | + | x - 2 | + | x - 3 | \geq 6

Q. If x satisfies

| x - 1 | + | x - 2 | + | x - 3 | \geq 6

Q. If x satisfies |x - 1| + |x -2| + |x - 3|

\geq 6,

Q. If the distance between the points A(2, −2) and B(−1, x) is 5, then

(a) x = −3 or x = 4
(b) x = 3 or x = −4
(c) x = −6 or x = 2
(d) x = 6 or x = −2

f (x) = \frac{x^{2} - 6 x + 5}{x^{2} - 5 x + 6}

	Column-I		Column-II
(A)	If $- 1 < x < 1$ , then f(x) satisfies	(p)	0 < f(x) < 1
(B)	If $1 < x < 2$ , then f(x) satisfies	(q)	f(x) < 0
(C)	If $3 < x < 5$ , then f(x) satisfies	(r)	f(x) > 0
(D)	If $x > 5$ , then f(x) satisfies	(s)	f(x) < 1

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Inequalities Involving Modulus Function

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