Question

15\sqrt{x-7} -2\sqrt{9x-63} -9\sqrt{25x-175} =\sqrt{4x-24}

Answer 1

To solve the equation 15√(x-7) - 2√(9x-63) - 9√(25x-175) = √(4x-24), we can simplify the equation and solve for x.

Given equation:
15√(x-7) - 2√(9x-63) - 9√(25x-175) = √(4x-24)

First, let's simplify the square roots by simplifying the expressions inside them:

15√(x-7) - 2√(9x-63) - 9√(25x-175) = √(4x-24)

15√(x-7) - 2√(9(x-7)) - 9√(25(x-7)) = √(4(x-6))

Simplifying further:

15√(x-7) - 6√(x-7) - 15√(x-7) = 2√(x-6)

Combining like terms:

-6√(x-7) = 2√(x-6)

Now, we can square both sides of the equation to eliminate the square roots:

(-6√(x-7))^2 = (2√(x-6))^2

36(x-7) = 4(x-6)

36x - 252 = 4x - 24

32x = 228

x = 7.125

Therefore, the solution to the equation is x = 7.125.