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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
Consider the given inequation
`4x - 19 < (3x)/5 - 2 <= (-2)/5 + x, x ∈ R`
`=> 4x - 19 + 2 < (3x)/5 - 2 + 2 <= (-2)/5 + x + 2, x ∈ R`
`=> 4x - 17 < (3x)/5 <= x + 8/5, x ∈ R`
`=> 4x - (3x)/5 < 17 and (-8)/5 <= x - (3x)/5, x ∈ R `
`=> (20x - 3x)/5 < 17 and (-8)/5 <= (5x - 3x)/5, x ∈ R`
`=> (17x)/5 < 17 and (-8)/5 <= (2x)/5, x ∈ R`
`=> x/5 < 1` and `-4 <= x, x ∈ R`
`=> x < 5` and `-4 <= x, x ∈ R`
`=> -4 ≤ x < 5; "where" x ∈ R`
The solution set can be represented on a number line as follows:
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