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Question
Solve the following inequation, write the solution set and represent it on the real number line.
`5x - 21 < (5x)/7 - 6 ≤ -3 3/7 + x, x ∈ R`
Solution
`5x - 21 < (5x)/7 - 6 ≤ -3 3/7 + x, x ∈ R`
`5x - 21 < (5x)/7 - 6`
`5x - (5x)/7 < -6 + 21`
`(35x - 5x)/7 < 15`
30x < 105
x < 3.5
`(5x)/7 - 6 ≤ -3 3/7 + x`
`(5x)/7 - x ≤ - 24/7 + 6`
`(5x - 7x)/7 ≤ (-24 + 42)/7`
–2x ≤ 18
x ≥ –9
`{x: -9 ≤ x < 7/2, x ∈ R}`
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