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solve the inequalities for real x (1)/(2...

solve the inequalities for real x `(1)/(2) ((3x)/(5) + 4 )ge (1)/(3) (x - 6)`

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The correct Answer is:
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Given inequation : `(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 30((3x + 20)/(10)) ge30((x-6)/(3))`
`rArr 3(3x + 20) ge 10(x - 6)`
`rArr 9x + 60 ge 10x - 60`
`rArr 9x ge 10x - 120 `
`rArr -x ge - 120`
`rArr xle 120 `
`:. Solution = ( - infty, 120] `
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