Answer:
To solve the equation -2|5x - 1| - 3 = -11, you can follow these steps:
Step 1: Add 3 to both sides of the equation to isolate the absolute value term:
-2|5x - 1| = -11 + 3
-2|5x - 1| = -8
Step 2: Divide both sides by -2. When you divide or multiply both sides of an inequality by a negative number, remember to reverse the inequality sign:
|5x - 1| = 4
Now, we have two cases to consider because the absolute value can be positive or negative:
Case 1: 5x - 1 is positive:
5x - 1 = 4
Solve for x:
5x = 4 + 1
5x = 5
x = 5/5
x = 1
Case 2: 5x - 1 is negative (we negate the absolute value):
5x - 1 = -4
Solve for x:
5x = -4 + 1
5x = -3
x = -3/5
So, there are two solutions:
x = 1 and x = -3/5.