Solve the inequality. Write the solution in interval notation.
|0.125x-4|>5
To solve the inequality, we can split it into two separate inequalities.
First, let's solve the inequality when 0.125x - 4 is positive:
0.125x - 4 > 5
Adding 4 to both sides:
0.125x > 9
Dividing both sides by 0.125:
x > 72
Next, let's solve the inequality when 0.125x - 4 is negative:
-(0.125x - 4) > 5
Expanding the negative sign:
-0.125x + 4 > 5
Subtracting 4 from both sides:
-0.125x > 1
Dividing both sides by -0.125 (remembering that we need to flip the inequality symbol since we are dividing by a negative number):
x < -8
Now we have two solutions: x > 72 and x < -8.
Combining the solutions in interval notation:
(-∞, -8) U (72, ∞)