Let's first simplify both sides of the inequality:
Left side: (5x+1)(3x-1) = 15x^2 + 5x - 3x - 1 = 15x^2 + 2x - 1
Right side: (4x-1)(x+2) = 4x^2 + 8x - x - 2 = 4x^2 + 7x - 2
Now, our inequality becomes:
15x^2 + 2x - 1 > 4x^2 + 7x - 2
Rearranging terms, we get:
15x^2 + 2x - 1 - 4x^2 - 7x + 2 > 0
Simplifying further, we get:
11x^2 - 5x + 1 > 0
Now, in order to solve this quadratic inequality, we can use different methods like graphing, factoring or using the discriminant.
After solving, we find the solution to the inequality is:
x < 5/22 or x > 1/11
Therefore, the inequality (5x+1)(3x-1)>(4x-1)(x+2) holds when x is less than 5/22 or greater than 1/11.
Let's first simplify both sides of the inequality:
Left side: (5x+1)(3x-1) = 15x^2 + 5x - 3x - 1 = 15x^2 + 2x - 1
Right side: (4x-1)(x+2) = 4x^2 + 8x - x - 2 = 4x^2 + 7x - 2
Now, our inequality becomes:
15x^2 + 2x - 1 > 4x^2 + 7x - 2
Rearranging terms, we get:
15x^2 + 2x - 1 - 4x^2 - 7x + 2 > 0
Simplifying further, we get:
11x^2 - 5x + 1 > 0
Now, in order to solve this quadratic inequality, we can use different methods like graphing, factoring or using the discriminant.
After solving, we find the solution to the inequality is:
x < 5/22 or x > 1/11
Therefore, the inequality (5x+1)(3x-1)>(4x-1)(x+2) holds when x is less than 5/22 or greater than 1/11.