Question

Solve the equation and check the solution.
7.1xplus 4equals6.1x
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Part 1
x​ =
  
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Answer 1

To solve the equation \( 7.1x + 4 = 6.1x \), follow these steps:

1. **Isolate the variable**: Start by moving all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 6.1x \) from both sides:

\[
7.1x - 6.1x + 4 = 0
\]

This simplifies to:

\[
1.0x + 4 = 0
\]

or

\[
x + 4 = 0
\]

2. **Solve for x**: Now, subtract 4 from both sides:

\[
x = -4
\]

So, the solution is:

\[
x = -4
\]

### Checking the solution:
Now, we can check the solution by substituting \( x = -4 \) back into the original equation:

**Original equation**:

\[
7.1(-4) + 4 = 6.1(-4)
\]

Calculating the left side:

\[
7.1 \times -4 + 4 = -28.4 + 4 = -24.4
\]

Calculating the right side:

\[
6.1 \times -4 = -24.4
\]

Both sides equal:

\[
-24.4 = -24.4
\]

Since both sides of the equation are equal, the solution \( x = -4 \) is verified to be correct.

Thus, the final answer is:

\[
\boxed{-4}
\]