Mathematics
Solve the inequation :
3z - 5 ≤ z + 3 < 5z - 9; z ∈ R.
Graph the solution set on the number line.
Linear Inequations
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Answer
Given,
3z - 5 ≤ z + 3 < 5z - 9
Solving L.H.S. of the above equation,
⇒ 3z - 5 ≤ z + 3
⇒ 3z - z ≤ 3 + 5
⇒ 2z ≤ 8
⇒ z ≤ 4 …..(i)
Solving R.H.S. of the above equation,
⇒ z + 3 < 5z - 9
⇒ 5z - z > 3 + 9
⇒ 4z > 12
⇒ z > 3 ……(ii)
From (i) and (ii) we get,
3 < z ≤ 4
∴ Solution set = {z : 3 < z ≤ 4, z ∈ R}.
Solution on the number line is :
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