Solve and graph the inequality.
StartAbsoluteValue x plus 8 EndAbsoluteValue greater than or equals 2
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Part 1
Choose the correct answer below.
A.x greater than or equals minus 6
x greater than or equals minus 6
B.x less than or equals minus 10 or x greater than or equals minus 6
x less than or equals minus 10 or x greater than or equals minus 6
C.x less than or equals minus 2 or x greater than or equals 2
x less than or equals minus 2 or x greater than or equals 2
D.negative 10 less than or equals x less than or equals minus 6
negative 10 less than or equals x less than or equals minus 6
To solve the inequality |x + 8| ≥ 2, we need to consider two cases.
Case 1: x + 8 ≥ 2
Solving this equation, we subtract 8 from both sides:
x ≥ -6
Case 2: -(x + 8) ≥ 2
Solving this equation, we multiply both sides by -1 and reverse the inequality sign:
x + 8 ≤ -2
Subtracting 8 from both sides:
x ≤ -10
Combining both cases, the solution to the inequality is:
x ≥ -6 or x ≤ -10
Graphically, the solution can be represented on a number line:
-∞-------------------(-10]------------[-6]------------------∞
where [-10] and [-6] are closed circles indicating inclusivity.