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in Linear Equations by (15.2k points)

Solve the system of in equation x – 2 ≥ 0, 2x – 5 ≤ 3.

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1 Answer

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by (15.7k points)

We have to find values of x for which both the equations hold true 

x – 2 ≥ 0 and 2x – 5 ≤ 3 

We will solve both the equations separately and then their intersection set will be solution of the system 

x – 2 ≥ 0 

⇒ x ≥ 2 

Hence x ∈ (2, ∞) 

Now, 2x – 5 ≤ 3 

⇒ 2x ≤ 3 + 5 

⇒ 2x ≤ 8 

⇒ x ≤ 4 

Hence x ∈ (-∞, 4) 

The intersection of set (2, ∞) and (-∞, 4) is (2, 4) 

Representing on number line

Hence solution set for given system of equation is x ∈ (2, 4)

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