Factor Quadratic Expression: Factor the quadratic expression. x² - 36 = (x - 6)(x + 6) Set Inequality: Set the inequality with the factored form. (x - 6)(x + 6) > 0 Determine Critical Points: Determine the critical points where the expression equals zero. x - 6 = 0 → x = 6 x + 6 = 0 → x = -6 Analyze Sign of Product: Analyze the sign of the product in each interval divided by the critical points: (-∞, -6), (-6, 6), and (6, ∞). Test x = -7 in (-∞, -6): (-7 - 6)(-7 + 6) = (-13)(-1) = 13 > 0 Test x = 0 in (-6, 6): (0 - 6)(0 + 6) = (-6)(6) = -36 0 Write Solution: Write the solution based on the sign analysis. The expression (x - 6)(x + 6) > 0 when x 6.

Algebra 1

Solve advanced linear inequalities

Full solution

x^2-36>0

Factor Quadratic Expression: Factor the quadratic expression. $x^2 - 36 = (x - 6)(x + 6)$
Set Inequality: Set the inequality with the factored form. $\newline$ (x - 6)(x + 6) > 0
Determine Critical Points: Determine the critical points where the expression equals zero. $\newline$ $x - 6 = 0 \rightarrow x = 6$ $\newline$ $x + 6 = 0 \rightarrow x = -6$
Analyze Sign of Product: Analyze the sign of the product in each interval divided by the critical points: $(-\infty, -6)$ , $(-6, 6)$ , and $(6, \infty)$ .
Test $x = -7$ in $(-\infty, -6)$ : (-7 - 6)(-7 + 6) = (-13)(-1) = 13 > 0
Test $x = 0$ in $(-6, 6)$ : (0 - 6)(0 + 6) = (-6)(6) = -36 < 0
Test $x = 7$ in $(6, \infty)$ : $(-6, 6)$ $1$
Write Solution: Write the solution based on the sign analysis. $\newline$ The expression (x - 6)(x + 6) > 0 when x < -6 or x > 6.