Solve and graph the inequality.
|x+2|>5
Choose the correct answer below.
A.x less than or equals minus 5 or x greater than or equals 5
x less than or equals minus 5 or x greater than or equals 5
B.negative 7 less than or equals x less than or equals 3
negative 7 less than or equals x less than or equals 3
C.x less than or equals minus 7 or x greater than or equals 3
x less than or equals minus 7 or x greater than or equals 3
D.x greater than or equals 3
x greater than or equals 3
The correct answer is C. x less than or equals -7 or x greater than or equals 3.
To solve the inequality |x+2| > 5, we have to consider two cases separately:
Case 1: x+2 > 5
In this case, we isolate x on one side of the inequality:
x > 5 - 2
x > 3
Case 2: -(x+2) > 5
In this case, we isolate x on one side of the inequality:
x+2 < -5
x < -5 - 2
x < -7
Thus, the solution to the inequality is x less than or equals -7 or x greater than or equals 3.
To graph this solution, we represent the solution on a number line with -7 and 3 as the boundary points, and shade the regions to the left of -7 and to the right of 3.