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Question
Solve the following inequation, write down the solution set and represent it on the real number line.
`-3 + x ≤ (7x)/2 + 2 < 8 + 2x, x ∈ I`
Solution
Given: `-3 + x ≤ (7x)/2 + 2 < 8 + 2x, x ∈ I`
Then, `-3 + x ≤ (7x)/2 + 2`
`\implies -3 - 2 ≤ (7x)/2 - x`
`\implies - 5 ≤ (7x - 2x)/2`
`\implies` –10 ≤ 5x
`\implies` – 2 ≤ x or x ≥ – 2
And `(7x)/2 + 2 < 8 + 2x`
`\implies (7x)/2 - 2x < 8 - 2`
`\implies (7x - 4x)/2 < 6`
`\implies` 3x < 12
`\implies` x < 4
`\implies` – 2 ≤ x < 4
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