58. Please solve the following equation.        0.3 (x – 2) = 0.1 (4 + x)*1 point54.432.4

1. Break Down the Problem

We need to solve the equation: $0.3 (x - 2) = 0.1 (4 + x)$

2. Relevant Concepts

We will use algebraic manipulation to isolate $x$. The steps will involve distributing the constants on both sides and then solving for $x$.

3. Analysis and Detail

1. Distribute both sides of the equation: $0.3x - 0.6 = 0.1(4) + 0.1x$ $0.3x - 0.6 = 0.4 + 0.1x$

2. Rearranging the equation: $0.3x - 0.1x = 0.4 + 0.6$ $0.2x = 1.0$

3. Solve for $x$: $x = \frac{1.0}{0.2}$ $x = 5$

4. Verify and Summarize

To verify, substitute $x = 5$ back into the original equation:

• Left side: $0.3(5 - 2) = 0.3 \times 3 = 0.9$
• Right side: $0.1(4 + 5) = 0.1 \times 9 = 0.9$

Both sides are equal, confirming that our solution is correct.

Final Answer

The solution to the equation is: $\boxed{5}$