Solve the inequality. Use algebra to solve the corresponding equation.
-$$x ^ { 2 } - 6 x - 7

Question

Solve the inequality. Use algebra to solve the corresponding equation.
-$$x ^ { 2 } - 6 x - 7 < 0$$
A) $( - \infty , - 1 )$
B) $( 7 , \infty )$
C) $( - 1,7 )$
D) $( - \infty , - 1 ) \cup ( 7 , \infty )$

Quizplus · Accepted Answer

To solve the inequality $x^2 - 6x - 7 < 0$, first solve the corresponding equation $x^2 - 6x - 7 = 0$. Factoring or using the quadratic formula yields the roots $x = -1$ and $x = 7$. These roots divide the number line into three intervals: $(-\infty, -1)$, $(-1, 7)$, and $(7, \infty)$. Testing values from each interval in the original inequality shows that the inequality holds for $x$ values in the interval $(-1, 7)$.

Solve the Inequality x2−6x−7<0x ^ { 2 } - 6 x - 7 < 0x2−6x−7<0

Solve the Inequality $x ^ { 2 } - 6 x - 7 < 0$