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Mathematics

If 5x - 3 ≤ 5 + 3x ≤ 4x + 2, express it as a ≤ x ≤ b and then state the values of a and b.

Linear Inequations

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Answer

Given,

⇒ 5x - 3 ≤ 5 + 3x ≤ 4x + 2

Solving L.H.S. of the equation,

⇒ 5x - 3 ≤ 5 + 3x

⇒ 5x - 3x ≤ 5 + 3

⇒ 2x ≤ 8

⇒ x ≤ 4 ……..(i)

Solving R.H.S. of the equation,

⇒ 5 + 3x ≤ 4x + 2

⇒ 3x - 4x ≤ 2 - 5

⇒ -x ≤ -3

⇒ x ≥ 3 …….(ii)

From (i) and (ii) we get,

3 ≤ x ≤ 4

Comparing above equation with a ≤ x ≤ b we get,

a = 3 and b = 4.

Hence, a = 3 and b = 4.

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