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Question
Solve the following inequation and represent the solution set on the number line:
4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R
Solution
The Given inequation is
`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x`, x ∈ R
`=> (4x - 19) < (3x - 10)/5 <= (-2 + 5x)/5`
`=> 5(4x - 19) < 3x - 10 < -2 + 5x`
`=> 20x - 95 < 3x - 10 <= -2 + 5x`
Solving `20x - 95 < 3x - 10`
`=> 17x < 85`
`=> x < 5`
Solving 3x - 10 <= -2 + 5x
`=> -2x <= 8`
`=> -x <= 4`
`=> x >= -4`
So the solution set = `{x : -4 <= x < 5, x in R}`
Representation on the Number line
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