Algebra-1

To solve the inequality |7a - 1| - 7 < -1, we can begin by adding 7 to both sides:

|7a - 1| < 6

Now, we can break it down into two cases:

Case 1: 7a - 1 is nonnegative (i.e., 7a - 1 ≥ 0)
In this case, the absolute value |7a - 1| is equal to 7a - 1, so we have:
7a - 1 < 6

Solving this inequality, we get:
7a < 6 + 1
7a < 7
a < 1

Case 2: 7a - 1 is negative (i.e., 7a - 1 < 0)
In this case, the absolute value |7a - 1| is equal to -(7a - 1), so we have:
-(7a - 1) < 6

Simplifying this inequality, we get:
-7a + 1 < 6

Subtracting 1 from both sides of the inequality, we have:
-7a < 6 - 1
-7a < 5

Dividing both sides of the inequality by -7 reverses the inequality sign:
a >

So the solution to the inequality |7a - 1| - 7 < -1 is:
a < 1 or a >

Comparing the solution to the given answer choices:

A. No solution
B. All real numbers
C. -1 < a <

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