Answer:
A
Step-by-step explanation:
Given inequality:
[tex]|x + 2| + 7 > 10[/tex]
Isolate the absolute value on one side of the inequality:
[tex]\implies |x + 2| + 7 -7 > 10-7[/tex]
[tex]\implies |x + 2| > 3[/tex]
Apply the absolute rule: If |u| > a, a > 0 then u < -a or u > a
[tex]\underline{\rm Case\; 1}\\\\\begin{aligned}x+2& < -3\\x+2-2& < -3-2\\x& < -5\end{aligned}[/tex] [tex]\underline{\rm Case\; 2}\\\\\begin{aligned}x+2& > 3\\x+2-2& > 3-2\\x& > 1\end{aligned}[/tex]
To graph the solution on a number line:
- Place an open circle at -5 and draw a line to the left with an arrow at the end.
- Place an open circle at 1 and draw a line to the right with an arrow at the end.
