\(x^2 - x - 4 ≤ 2\) Subtract two from both sides to rewrite it in the quadratic standard form: = \(x^2 - x - 4 - 2 ≤ 2 - 2\) = \(x^2 - x - 6 ≤ 0\) Now set it = 0 and factor and solve like normal. = \(x^2 - x\) - 6=0 = \((x - 3)(x + 2)\)=0 \(x\) + 2 = 0 or \(x\) - 3 = 0 \(x\) = -2 or \(x\) = 3 So the two zeros are -2 and 3, and will mark the boundaries of our answer interval. To find out if the interval is between -2 and 3, or on either side, we simply take a test point between -2 and 3 (for instance, \(x\) = 0) and evaluate the original inequality. = \(x2 - x - 4 ≤ 2\) = \((0)^2 - (0) - 4 ≤ 2\) = \(0 - 0 - 4 ≤ 2\) \(−4 ≤ 2\) Since the above is a true statement, we know that the solution interval is between -2 and 3, the same region where we picked our test point. Since the original inequality was less than or equal, we include the endpoints. ∴ \(-2 ≤ x ≤ 3.\)