Question

What is the solution to the equation 1.26(x-7.352)=6.426 when solving for x

12.452

-2.252

15.44876

15.038

Answer 1

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

1. **Distribute the 1.26**:
\[
1.26x - 1.26 \cdot 7.352 = 6.426
\]
Calculate \( 1.26 \cdot 7.352 \):
\[
1.26 \cdot 7.352 \approx 9.263
\]
So the equation becomes:
\[
1.26x - 9.263 = 6.426
\]

2. **Add 9.263 to both sides**:
\[
1.26x = 6.426 + 9.263
\]
Calculate the right side:
\[
6.426 + 9.263 \approx 15.689
\]
Now we have:
\[
1.26x = 15.689
\]

3. **Divide both sides by 1.26**:
\[
x = \frac{15.689}{1.26} \approx 12.450
\]

Rounding to three significant figures gives us \( x \approx 12.452 \).

Therefore, the solution for \( x \) is **12.452**.