Final answer:
To solve the inequality by graphing, convert the inequality to the form x² - 6x + 3 < 0, find the roots using the quadratic formula, and then determine the interval for x that satisfies the inequality. The correct answer is option D).
Step-by-step explanation:
To solve the inequality x² - 6x < -3 by graphing, we first bring the inequality to standard quadratic form: Step 1: Add 3 to both sides to get: x² - 6x + 3 < 0. Step 2: Factor the quadratic equation (if possible) or use the quadratic formula. In this case, the quadratic doesn't factor nicely, so we use the quadratic formula where a = 1, b = -6, and c = 3.
Step 3: The solutions to the equation x² - 6x + 3 = 0 are the critical points which divide the number line into intervals. We use these points to determine the intervals where the inequality is true. The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a). Substituting our values in gives us two solutions x ≈ 0.55 and x ≈ 5.45.
These solutions are not exact roots of the equation but approximate to two decimal places. Step 4: Plot these two points on a graph and test an interval to find where the inequality is true. After graphing, you find the solution is D) x < -1.45 or x > 7.45.