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Question
Solve `(2x + 1)/(2) + 2(3 - x) ≥ 7, x ∈ "R"`. Also graph the solution set on the number line
Solution
`(2x + 1)/(2) + 2(3 - x) ≥ 7, x ∈ "R"`
⇒ `(2x + 1)/(2) + 6 - 2x ≥ 7`
⇒ `(2x + 1)/(2) - 2x ≥ 7 - 6`
⇒ `(2x + 1 - 4x)/(2) ≥ 1`
⇒ 2x + 1 - 4 x ≥ 2
⇒ -2x ≥ 2 - 1
⇒ -2x ≥ 1
⇒ `-x ≥ (1)/(2)`
⇒ `x ≤ - (1)/(2)`
∴ Solution set `{x : x ∈ "R", x ≤ - (1)/(2)}`
Solution on number line:
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