Solve the inequality. Write the solution set in interval notation.
-$x ^ { 2 } - 6 x \leq - 8$
A) $( - \infty , - 4 ] \cup [ - 2 , \infty )$
B) $[ 2,4 ]$
C) $[ - 4 , - 2 ]$
D) $( - 4 , - 2 )$

Question

Quizplus · Accepted Answer

First, rearrange the inequality to standard form: $x^2 - 6x + 8 \leq 0$. Factoring gives $(x - 2)(x - 4) \leq 0$. The critical points are x = 2 and x = 4. Testing intervals around these points shows the inequality holds for $2 \leq x \leq 4$, hence the solution is $[2, 4]$.

Solve the Inequality x2−6x≤−8x ^ { 2 } - 6 x \leq - 8x2−6x≤−8

Solve the Inequality $x ^ { 2 } - 6 x \leq - 8$