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If 1/2 (3/5 x+4) ge 1/3 (x-6) , x in R ,...

If `1/2 (3/5 x+4) ge 1/3 (x-6) , x in R` , then

A

`[120, oo]`

B

`(-oo, 120]`

C

`[0, 120]`

D

`[-120, 0]`

Text Solution

Verified by Experts

The correct Answer is:
B
We have,
`(1)/(2) ((3x)/(5) + 4) ge (1)/(3)(x-6)`
`rArr (1)/(2) ((3x+20)/(5) ) ge (1)/(3)(x-6)`
`rArr (3x + 20)/(10) ge (x-6)/(3)`
`rArr 3(3x + 20) ge 10 (x-6) " " ["Multiplying both sides by 30 i.e the LCM of 10 and 3"]`
`rArr 9x+60 ge 10x-60`
`rArr 9x-10x ge -60-60`
`rArr -x ge -120 `
`rArr x le 120`
`rArr x in (-oo, 120]`
Hence, the solution set of the given inequation is `(-oo, 120]`, REMARK The solution set of simultaneous inequations is the intersection of their solution sets.
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OBJECTIVE RD SHARMA ENGLISH-ALGEBRAIC INEQUATIONS-Exercise
  1. If 1/2 (3/5 x+4) ge 1/3 (x-6) , x in R , then

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  2. The solution set of the inequation (x+4)/(x-3) le2, is

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  3. If (3(x-2))/(5)gt=(5(2-x))/(3), then x belongs to the interval

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  4. solve the inequation (2x+4)/(x-1) ge 5 and represent this solution on ...

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  5. The solution set of the inequation (4x + 3)/(2x-5) lt 6, is

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  6. The number of integral solutions of 2(x+2)gt x^(2)+1, is

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  7. If |3x + 2| lt 1, then x belongs to the interval

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  8. The solution set of the inequation |2x - 3| < |x+2|, is

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  9. The solution set of the inequation |(3)/(x)+1| gt 2, is

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  10. The solution set of the inequation 0 lt |3x+ 1|lt (1)/(3), is

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  11. The solution set of the inequation (x^2-3x+4)/(x+1) > 1, x in RR, is

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  12. The solution set of the inequation... 2/(|x-4|) >1,x != 4 is ...

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  13. What is the solution set of the inequality (1)/(|x|-3) lt (1)/(2) ?

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  14. The solution set of the inequation |(2x-1)/(x-1)| gt 2, is

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  15. The solution set of the inequation (|x-2|)/(x-2) lt 0, is

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  16. Write the solution set of inequation |x+1/x|> 2.

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  17. If the complete set of value of x satisfying |x-1| + |x-3| ge (-oo, a ...

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  18. The solution set of x^(2) + 2 le 3x le 2x^(2)-5, is

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  19. Writhe the set of values of x satisfying |x-1|lt=3\ a n d\ |x-1|lt=1.

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  20. The solution set of the inequation x^(2) + (a +b) x +ab lt 0, " wher...

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  21. The number of integral solutions of x^(2)-3x-4 lt 0, is

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