Solve the inequality. Write the solution in interval notation.
|0.5x - 6| > 7
The solution is __
(Type your answer in interval notation.)
To solve the inequality |0.5x - 6| > 7, we will consider two cases.
Case 1: 0.5x - 6 > 7
Adding 6 to both sides, we get:
0.5x > 13
Now divide both sides by 0.5 to isolate x:
x > 26
Case 2: 0.5x - 6 < -7
Adding 6 to both sides, we get:
0.5x < -1
Now divide both sides by 0.5, keeping in mind that when we divide by a negative number, the inequality sign flips:
x < -2
Therefore, the solution is x < -2 or x > 26.
In interval notation, the solution is (-∞, -2) ∪ (26, ∞).
To solve the inequality |0.5x - 6| > 7, we need to consider two cases - when the expression inside the absolute value is positive and when it is negative.
Case 1: 0.5x - 6 > 7
Adding 6 to both sides, we have:
0.5x > 13
Dividing both sides by 0.5, we get:
x > 26
Case 2: -(0.5x - 6) > 7
Expanding the expression inside the absolute value and simplifying, we have:
-0.5x + 6 > 7
Subtracting 6 from both sides, we get:
-0.5x > 1
Dividing both sides by -0.5, we have to flip the inequality sign since we are dividing by a negative number:
x < -2
So the solutions to the inequality |0.5x - 6| > 7 are x > 26 and x < -2.
Writing the solutions in interval notation:
(-∞, -2) U (26, ∞)