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Question
Solve the following inequation, write the solution set and represent it on the number line.
`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`
Solution
`-3 (x - 7) ≥ 15 - 7x > (x + 1)/3, x ∈ R`
`\implies -3 (x - 7) ≥ 15 - 7x` and `15 - 7x > (x + 1)/3`
`\implies` –3x + 21 ≥ 15 – 7x and 45 – 21 > x + 1
`\implies` 4x ≥ –6 and 44 > 22x
`\implies x ≥ (-3)/2` and `2 > x`
`\implies` x ≥ –1.5 and 2 > x
The solution set is {x : x ∈ R, –1.5 ≤ x < 2}
The solution set is represented on number line as follows:
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