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

Question

7
|
2
𝑥
−
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
7
|
2
𝑥
−
1
|
+
4
=
3
has 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. Divide both sides by 7: \[ |2x - 1| = -\frac{1}{7} \]

Since the absolute value cannot be negative, the equation \( |2x - 1| = -\frac{1}{7} \) has no solutions. Thus, the number of solutions is:

\[ \boxed{0} \]