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Question
Solving the following inequation, write the solution set and represent it on the number line. – 3(x – 7)≥15 – 7x > `(x + 1)/(3)` , n ∈R
Solution
– 3(x – 7)≥15 – 7x > `(x + 1)/(3)` , n ∈R
– 3(x – 7)≥15 – 7x ⇒ 3x + 21 ≥ 15 - 7x
–3x + 7x ≥ 15 – 21 ⇒ 4x ≥ –6
⇒ `x ≥ (-6)/(4)`
⇒ `x ≥ (-3)/(2)`
⇒ `(-3)/(2) ≤ x`
and
`15 - 7x > (x + 1)/(3)`
⇒ 45 - 21x > x + 1
⇒ 45 - 1 > x + 21x
⇒ 44 > 22x
2 > x ⇒ x = 2
∴ `(-3)/(2) ≤ x < 2, x ∈ "R"`
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