Question

Let T = x:x+5/x-7 -5 = 4x-40/13-x . Is T an empty set ? Justify your answer

Answer 1

Given: The set T = { x:x+5/x-7 -5 = 4x-40/13-x }

To find: Is T an empty set ? Justify your answer.

Solution:

• So we have provided with a set T, which have:

                T = { x : (x + 5 / x - 7) - 5 = (4x - 40 / 13 - x) }

• So the equation given is: (x + 5 / x - 7) - 5 = (4x - 40 / 13 - x)

• Solving this equation, we get:

                (x + 5 / x - 7) - 5 = (4x - 40 / 13 - x)

                (x + 5 / x - 7) - (4x - 40 / 13 - x)  = 5

• Now cross multiplying, we get:

                { (x + 5) × (13 - x) - (4x - 40) × (x - 7) } / (13 - x) × (x - 7) = 5

• Now multiplying the brackets, we get:

                {13x - x² + 65 - 5x - 4x² + 40x + 28x - 280} / {13x - x² - 91 + 7x} = 5

• Now adding similar terms, we get:

                {-5x² + 76x - 215 } / { -x² + 20x - 91 } = 5

• Now simplifying, we get:

                -5x² + 76x - 215 = -5x² + 100x - 455

                455 - 215 = 24x

                240 = 24x

                x = 240 / 24

                x = 10

• So set T contains an element which is 10.

Answer:

              So the set T is not an empty set as it has an element '10'.