Solve the following inequality and graph the solution: \[ (x+3)(x-4)<0 \] Write the solution in interval notation

To solve the inequality \((x+3)(x-4)<0\), we first identify the critical points by setting the expression equal to zero: 1. \(x + 3 = 0\) gives \(x = -3\) 2. \(x - 4 = 0\) gives \(x = 4\) These critical points split the number line into three intervals: \((-∞, -3)\), \((-3, 4)\), and \((4, ∞)\). Next, we test a point from each interval: - For \((-∞, -3)\), let's test \(x = -4\): \(((-4)+3)((-4)-4) = (-1)(-8) = 8 > 0\) (not part of the solution) - For \((-3, 4)\), let's test \(x = 0\): \((0+3)(0-4) = (3)(-4) = -12 < 0\) (this interval works) - For \((4, ∞)\), let's test \(x = 5\): \((5+3)(5-4) = (8)(1) = 8 > 0\) (not part of the solution) Thus, the solution to the inequality is the interval where the product is negative: \((-3, 4)\). In interval notation, the solution is \((-3, 4)\). To graph the solution, you'd draw a number line, marking -3 and 4 with open circles (to denote that these points are not included), and shade the region between them.