Question

.
(30x - 9)/(x-2) ≥ 25(x+2)​

Answer 1

Given: The expression (30x - 9)/(x-2) ≥ 25(x+2)​

To find: The value of x?

Solution:

• Now we have given the expression as:

              (30x - 9)/(x-2) ≥ 25(x+2)​

• Solving the equation, we get:

• Cross multiplying the denominator:

              (30x - 9) ≥ 25(x+2)​ (x-2)

• Solving further, we get:

              (30x - 9) ≥ 25(x^2 - 2^2)

              (30x - 9) ≥ 25(x^2 - 4)

              (30x - 9) ≥ 25x^2 - 100

              0 ≥ 25x^2 - 30x - 100 + 9

              25x^2 - 30x - 91 ≤ 0

• Let 25x^2 - 30x - 91 = 0

• So by middle term splitting, we get:

              25x^2 - 65x + 35x - 91 = 0

              5x(5x - 13) + 7(5x - 13) = 0

              (5x + 7)(5x - 13) = 0

              x = -7/5 or 13/5

Answer:

         So the value of x is -7/5 or 13/5.