Question

What is the absolute value of 7 * 2x - 1 + 4 = 3 it has how many solutions

Answer 1

To solve the equation \( |7(2x - 1) + 4| = 3 \), let's first simplify the expression inside the absolute value.

1. Start with the expression inside the absolute value:
\[
7(2x - 1) + 4
\]
Distributing the \(7\):
\[
= 14x - 7 + 4 = 14x - 3
\]
So the equation is now:
\[
|14x - 3| = 3
\]

2. The absolute value equation \( |A| = B \) implies two cases:
\[
A = B \quad \text{or} \quad A = -B
\]
Now applying this to our equation:
- Case 1:
\[
14x - 3 = 3
\]
Solving for \(x\):
\[
14x = 6 \quad \Rightarrow \quad x = \frac{6}{14} = \frac{3}{7}
\]

- Case 2:
\[
14x - 3 = -3
\]
Solving for \(x\):
\[
14x = 0 \quad \Rightarrow \quad x = 0
\]

3. Thus, we have the solutions:
\[
x = \frac{3}{7} \quad \text{and} \quad x = 0
\]

In summary, the absolute value equation \( |7(2x - 1) + 4| = 3 \) has **2 solutions**: \( x = \frac{3}{7} \) and \( x = 0 \).