To solve this inequality, we first need to find the roots of the quadratic expression in the numerator.
The roots can be found by setting the numerator equal to 0:
7x^2 + 6x - 1 = 0
Using the quadratic formula, we find that the roots are x = 1/7 and x = -1.
Next, we need to determine the sign of the expression for different ranges of x.
For x < -1, the expression 7x^2 + 6x - 1 is negative and 5-x is also negative. The fraction of two negative values will be positive.
For -1 < x < 1/7, the expression 7x^2 + 6x - 1 is positive and 5-x is negative. The fraction of a positive and a negative value will be negative.
For x > 1/7, both 7x^2 + 6x - 1 and 5-x are positive. The fraction of two positive values will be positive.
Therefore, the solution to the inequality is x < -1 or x > 1/7.
To solve this inequality, we first need to find the roots of the quadratic expression in the numerator.
The roots can be found by setting the numerator equal to 0:
7x^2 + 6x - 1 = 0
Using the quadratic formula, we find that the roots are x = 1/7 and x = -1.
Next, we need to determine the sign of the expression for different ranges of x.
For x < -1, the expression 7x^2 + 6x - 1 is negative and 5-x is also negative. The fraction of two negative values will be positive.
For -1 < x < 1/7, the expression 7x^2 + 6x - 1 is positive and 5-x is negative. The fraction of a positive and a negative value will be negative.
For x > 1/7, both 7x^2 + 6x - 1 and 5-x are positive. The fraction of two positive values will be positive.
Therefore, the solution to the inequality is x < -1 or x > 1/7.