Question

What is the solution to the equation 1.26(x−7.352)=6.426 when solving for x ?(1 point)
Responses

−2.252
negative 2.252

15.038
15.038

12.452
12.452

15.44876

Answer 1

To solve the equation \( 1.26(x - 7.352) = 6.426 \), we'll follow these steps:

1. **Distribute** the \( 1.26 \) on the left side of the equation:
\[
1.26x - 1.26 \times 7.352 = 6.426
\]
Calculate \( 1.26 \times 7.352 \):
\[
1.26 \times 7.352 \approx 9.25
\]
So the equation simplifies to:
\[
1.26x - 9.25 = 6.426
\]

2. **Add \( 9.25 \)** to both sides:
\[
1.26x = 6.426 + 9.25
\]
Calculate \( 6.426 + 9.25 \):
\[
6.426 + 9.25 \approx 15.676
\]
So now we have:
\[
1.26x = 15.676
\]

3. **Divide by \( 1.26 \)** to isolate \( x \):
\[
x = \frac{15.676}{1.26}
\]
Calculate \( \frac{15.676}{1.26} \):
\[
x \approx 12.4381
\]

Based on the closest answer from the options provided:
- The closest answer is **12.452**.