Question

Solve and graph the solution set on a real number line: x² - x > 20

Answer 1

To solve the inequality x² - x > 20 and graph the solution set on a real number line, factor the quadratic expression and use a sign chart to determine the solution set.

Step-by-step explanation:

To solve the inequality x² - x > 20 and graph the solution set on a real number line, we first rearrange the inequality to x² - x - 20 > 0. Then, we factor the quadratic expression to (x - 5)(x + 4) > 0. Now, we can use a sign chart to determine the solution set:

• When x < -4, both factors are negative, so the inequality is false.
• When -4 < x < 5, the first factor is negative while the second factor is positive, so the inequality is true.
• When x > 5, both factors are positive, so the inequality is true.

Therefore, the solution set is (-∞, -4) ∪ (5, ∞), which can be graphed on a real number line.