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If ||x-1|-2|=5, then find x....

If `||x-1|-2|=5`, then find x.

A

`5,-4`

B

`-7, 4`

C

`-8,6`

D

`8,-6`

Text Solution

Verified by Experts

The correct Answer is:
D
`|x-1|-2=+-5`
`|x-1|=7,-3`
Case-I: When `|x-1|=7 rArr x-1 =+-7 rArr x=8,-6`
Case II: When `|x-1|=-3` (reject)
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ALLEN-BASIC MATHS LOGARITHIM TRIGNOMETRIC RATIO AND IDENTITIES AND TRIGNOMETRIC EQUATION -ILLUSTRATIONS
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  2. If |x-1|+|x+1|=2, then find x.

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  3. If x satisfies |x-1|+x|x-2|+|x-3|ge6, then A) 0 lexle4 B) xle-2 or...

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  4. Solve for x: a) ||x-1|+2|le4|, b) (x-4)/(x+2) le |(x+2)/(x-1)|

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  5. The equation |x|+|x/(x-1)|=x^(2)/(|x-1|) is always true for x belongs ...

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  6. Solve for x, if sqrt(x^(2)-3x+2) lt x-2

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  7. If log(4)m=1.5, then find the value of m.

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  8. If log(5)p = a and log(2)q=a, then prove that (p^(4)q^(4))/(100) = 100...

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  9. The value of N satisfying log(a)[1+log(b){1+log(c)(1+log(p)N)}]=0 is

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  10. Find the value of 2log2/5 +3 log25/8 -log 625/128

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  11. If log(theta)x-log(theta)y= a, log(theta)y-log(theta)z=b and log(theta...

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  12. If a^(2)+b^(2)=23ab, then prove that log(a+b)/5=1/2(loga+logb)

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  13. If log(a)x = p and log(b)x^(2) =q, then log(x)sqrt(ab) is equal to (wh...

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  14. If a,b,c are distinct real number different from 1 such that (log(b)...

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  15. Evaluate: 81^(1//log(5)3) + 27^(log(9)36) + 3^(4//log(l)9)

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  17. Solve for x: log(2)x le 2/(log(2)x-1)

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  18. Solve the equation: log(2x+3)x^(2) lt log(2x)(2x+3)

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  19. Solve for x:2^(x+2) gt (1/4)^(1/x)

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  20. Solve for x: (1.25)^(1-x) gt (0.64)^(2(1+sqrt(x))

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