Solve the absolute value equation 7|2x−1|+4=3

Question

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
solution(s).

Answer 1

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

1. Subtract 4 from both sides:

\[ 7|2x - 1| = 3 - 4 \]

This simplifies to:

\[ 7|2x - 1| = -1 \]

2. Now divide both sides by 7:

\[ |2x - 1| = -\frac{1}{7} \]

The absolute value of any expression is always non-negative (i.e., \( |A| \geq 0 \) for any \( A \)). Since we have \( |2x - 1| = -\frac{1}{7} \) which is negative, there are no solutions to this equation.

Therefore, the answer is:

\[ \text{0 for no solutions.} \]