Solve the absolute value equation 7|2x−1|+4=3 to determine how many solutions exist. Enter 1 for one solution, 2 for two solutions, or 0 for no solutions.(1 point) The absolute value equation 7|2x−1|+4=3 has blank solution(s).

Answer 1

To solve the equation \( 7|2x - 1| + 4 = 3 \), we first isolate the absolute value term.

1. Subtract 4 from both sides: \[ 7|2x - 1| = 3 - 4 \] \[ 7|2x - 1| = -1 \]

2. Since the absolute value expression \( |2x - 1| \) is always non-negative, the left-hand side \( 7|2x - 1| \) can never be negative. Therefore, \( 7|2x - 1| = -1 \) has no solutions.

Thus, the absolute value equation \( 7|2x - 1| + 4 = 3 \) has 0 solutions.

The final answer is: \[ \text{0} \]