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Question
Solve the following inequation, write the solution set and represent it on the number line.
`-3(x - 7) >= 15 - 7x > (x+1)/3`, x ∉ R
Solution
`-3(x - 7) >= 15 - 7x > (x+1)/3`
`=> -3(x - 7)>= 15 - 7x` and `15 - 7x >(x+1)/3`
`=> -3x + 21 >= 15 - 7x` and 45 - 21x > x + 1
`=>4x >= -6` and 44 > 22x
`=> x >= (-3)/2` and 2 > x
`=> x >= -1.5 and 2 > x`
The solution set is `{x : x ∈ R, -1.5 <= x < 2}`
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