Algebra-1

To solve the inequality |3c - 4| < 12, we can break it down into two cases based on the absolute value expression.

Case 1: 3c - 4 ≥ 0 (when the absolute value is positive or zero)
In this case, the inequality becomes 3c - 4 < 12. Adding 4 to both sides of the inequality gives 3c < 16. Dividing both sides by 3 (since 3 is positive) gives c < , which is approximately 5.33.

Case 2: 3c - 4 < 0 (when the absolute value is negative)
In this case, the inequality becomes -(3c - 4) < 12. Simplifying the inequality gives -3c + 4 < 12. Subtracting 4 from both sides of the inequality gives -3c < 8. Dividing both sides by -3 (since -3 is negative) reverses the inequality sign, giving c > , which is approximately -2.67.

Combining the results from the two cases, we have < c