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(x)/(4) lt ((5x - 2))/(3) - ((7x - 3))/(...

`(x)/(4) lt ((5x - 2))/(3) - ((7x - 3))/(5)`

Text Solution

Verified by Experts

The correct Answer is:
N/a
Given inequation :
`(x)/(4) lt ((5x - 2))/(3) - ((7x - 3))/(5)`
` rArr (x) /(4) lt (5(4x - 2) - 3(7x - 3))/(15) `
` rArr (x)/(4)lt ( 25x - 10 - 21x + 9 )/(15) `
`rArr (x)/(4)lt (4x - 1)/(15) `
`rArr 60 xx (x)/(4) lt (60(4x -1))/(15)`
`rArr 15x lt 4(4x - 1 ) rArr 15x lt 16x - 4 `
`rArr -x - 4 `
`rArr x gt 4 `
`:.` Solution = (4, `infty` )
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Solve the inequalities for real x:(x)/(4)<((5x-2))/(3)-((7x-3))/(5)

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Knowledge Check

  • If (3x -2)/(3) + ( 2x + 3)/(2) = x + (7)/(6), then the value of (5x - 2)/(4) is

    A
    `(1)/(4)`
    B
    `(-1)/(12)`
    C
    `(1)/(12)`
    D
    `(-1)/(3)`

  • If f (x) = (3x + 4)/( 5x -7), g (x) = (7x +4)/(5x -3) then f [g(x)]=

    A
    `-41`
    B
    x
    C
    `-x`
    D
    41

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    Solve : (5x)/(4)gt (4x-1)/(3) and 4x + 3 lt (2x + 1)/(3)

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    ((5x+3)-(4x-2))/((5x+3)+(x-1))=(7)/(4)

    (3x-4)/(7)+(7)/(3x-4)=(5)/(2)

    Solve (4x-3)/(2-x) gt -5 3 - 2x lt 4 5x - 3 ge 7

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