Question

solve for x.
4(x + 1)(x + 3) ≥ 0
write a compound inequality like 1 < x < 3 or like x < 1 or x > 3.

Explanation:

Step1: Analyze the coefficient and roots

The inequality is \(4(x + 1)(x + 3)\geq0\). The coefficient of the quadratic part (when expanded) is \(4\), which is positive. The roots of the equation \(4(x + 1)(x + 3)=0\) are found by setting each factor equal to zero: \(x+1 = 0\) gives \(x=-1\), and \(x + 3=0\) gives \(x=-3\).

Step2: Determine the sign intervals

For a quadratic function \(y = a(x - r_1)(x - r_2)\) with \(a>0\), the graph opens upwards. So, the function is non - negative (\(\geq0\)) when \(x\leq r_2\) or \(x\geq r_1\) (where \(r_2

Answer:

\(x\leq - 3\) or \(x\geq - 1\)