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Question
Solve the following inequation. Write down the solution set and represent it on the real number line.
–5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R
Solution
Given: –5(x – 9) ≥ 17 – 9x > x + 2, x ∈ R
`\implies` –5x + 45 ≥ 17 – 9x and 17 – 9x > x + 2
`\implies` 9x – 5x ≥ 17 – 45 and – x – 9x > 2 – 17
`\implies` 4x ≥ – 28 and – 10x > – 15
`\implies` x ≥ – 7 and x < `15/10`
`\implies` x ≥ – 7 and x < `3/2`
Hence solution set `x ∈ [-7, 3/2)` as x ∈ R
Representation on number line
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