1.

Solve the system of inequations `-5le(2-3x)/(4)le9`.

Answer» We have
` -5le(2-3x)/(4)le9rArr -5le(2-3x)/(4)le9`.
Now, `-5le(2-3x)/(4)rArr -20le2-3x` [mutliplying both sides by 4]
`rArr -22le-3x` [adding -2 on both sides]
`rArr 22le3x` [multiplying both sides by -1]
`rArr 3xle22`
`rArr x le(22)/(3)` [dividing both sides by 3]
`rArr x in (-oo,(22)/(3)]`.

And, `(2-3x)/(4)le9 rArr 2-3x le 36` [multiplying both sides by 4]
`rArr -3x le34`
`rArr x ge 9-(34)/(3)` [dividing both sides by -3]

`rArrx in[(-34)/(3),oo)`.
`therefore " solution set " =(-oo,(22)/(30)]nn[(-34)/(3),oo)=[(-34)/(3),(22)/(3)]`.


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