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Question
Solve the following linear in-equation and graph the solution set on a real number line :
`1/3 (2x - 1) < 1/4 (x + 5) < 1/6 (3x + 4)`, x ∈ R
Solution
`1/3 (2x - 1) < 1/4 (x + 5)`
4(2x - 1) < 3 (x + 5)
8x - 4 < 3x +15
8x - 3x < 15 + 4
5x < 19
x < `3 4/5`
and
`1/4 (x + 5) < 1/6 (3x + 4)`
6 (x + 5) < 4 (3x + 4)
6x + 30 < 12 x + 16
6x - 12x < 16 -30
-6x < -14
x > `2 1/3`
Solution set = `[2 1/3 < x < 3 4/5]`
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