Question

solve the inequality. graph the solution.\\(|x + 11| > 6\\)\
solve the inequality. select the correct choice below and fill in the answer boxes within your choice.\
\\(\bigcirc\\) a. \\(x < \square\\) or \\(x > \square\\)\
\\(\bigcirc\\) b. \\(\square < x < \square\\)\
\\(\bigcirc\\) c. the solution is all real numbers.\
\\(\bigcirc\\) d. there is no solution.\
choose the correct graph below.\
\\(\bigcirc\\) a. \\(\overleftarrow{\
ule{2cm}{0.15mm}}\\) -40 -35 -30 -25 -20 \\(\circ\\) -15 -10 \\(\circ\\) -5 0 \\(\overrightarrow{\
ule{0.5cm}{0.15mm}}\\)\
\\(\bigcirc\\) b. \\(\overleftarrow{\
ule{2cm}{0.15mm}}\\) -40 -35 -30 -25 -20 -15 -10 -5 0 \\(\overrightarrow{\
ule{0.5cm}{0.15mm}}\\)\
\\(\bigcirc\\) c. \\(\overleftarrow{\
ule{0.5cm}{0.15mm}}\\) -40 -35 -30 -25 -20 \\(\circ\\) -15 -10 \\(\circ\\) -5 0 \\(\overrightarrow{\
ule{0.5cm}{0.15mm}}\\)\
\\(\bigcirc\\) d. the graph contains no points.

Explanation:

Step1: Split absolute value inequality

For $|x+11|>6$, we split into two cases:
$x+11 > 6$ or $x+11 < -6$

Step2: Solve first inequality

Isolate $x$ by subtracting 11:
$x > 6 - 11$
$x > -5$

Step3: Solve second inequality

Isolate $x$ by subtracting 11:
$x < -6 - 11$
$x < -17$

Answer:

A. $x < -17$ or $x > -5$
A. <point>802 481</point> (the graph with open circles at -17 and -5, arrows pointing left from -17 and right from -5)