Question

question
solve the following inequality algebraically.
\\( x^2 + x - 20 \leq 0 \\)
answer attempt 1 out of 3

Explanation:

Step1: Factor the quadratic expression

$x^2 + x - 20 = (x + 5)(x - 4)$

Step2: Find critical points

Set $(x + 5)(x - 4) = 0$, so $x = -5$ or $x = 4$

Step3: Test intervals

Test $x < -5$: $(-)(-) = + > 0$ (not valid)
Test $-5 < x < 4$: $(+)(-) = - < 0$ (valid)
Test $x > 4$: $(+)(+) = + > 0$ (not valid)

Step4: Include critical points

Inequality is $\leq 0$, so include $x=-5$ and $x=4$

Answer:

$-5 \leq x \leq 4$ (or in interval notation: $[-5, 4]$)