Determine the values of x for the following inequality x2 – 3x – 28 < 0? – 4 < x < 7 4 < x < -7 - 4 < x < -7 4 < x < 7 None of these

To solve the inequality x^2 - 3x - 28 < 0, we first need to factor the quadratic expression on the left side of the inequality.

The quadratic x^2 - 3x - 28 factors to (x - 7)(x + 4).

Setting each factor equal to zero gives the potential turning points x = 7 and x = -4.

We now test the intervals determined by these turning points in the factored inequality:

For x < -4, both factors (x - 7) and (x + 4) are negative, so the product is positive. Therefore, the inequality is not satisfied for x < -4.

For -4 < x < 7, the factor (x - 7) is negative and the factor (x + 4) is positive, so the product is negative. Therefore, the inequality is satisfied for -4 < x < 7.

For x > 7, both factors (x - 7) and (x + 4) are positive, so the product is positive. Therefore, the inequality is not satisfied for x > 7.

So, the solution to the inequality x^2 - 3x - 28 < 0 is -4 < x < 7.