Question

What is the value of x in the equation 0.5x - 0.3(0.2x + 5) = 0.4x - 3?

Answer

Answer 1

To solve the equation \( 0.5x - 0.3(0.2x + 5) = 0.4x - 3 \), we will first simplify the left side of the equation.

1. Distribute the \( -0.3 \) across the terms inside the parentheses:

\[
0.5x - 0.3(0.2x + 5) = 0.5x - 0.3 \cdot 0.2x - 0.3 \cdot 5
\]

Calculating \( -0.3 \cdot 0.2x \) and \( -0.3 \cdot 5 \):

\[
= 0.5x - 0.06x - 1.5
\]

Now substitute back into the equation:

\[
0.5x - 0.06x - 1.5 = 0.4x - 3
\]

2. Combine like terms on the left side:

\[
(0.5x - 0.06x) - 1.5 = 0.4x - 3
\]

\[
0.44x - 1.5 = 0.4x - 3
\]

3. Next, isolate \( x \) by moving all terms involving \( x \) to one side and constant terms to the other side. Subtract \( 0.4x \) from both sides:

\[
0.44x - 0.4x - 1.5 = -3
\]

\[
0.04x - 1.5 = -3
\]

4. Now, add \( 1.5 \) to both sides:

\[
0.04x = -3 + 1.5
\]

\[
0.04x = -1.5
\]

5. Finally, divide both sides by \( 0.04 \):

\[
x = \frac{-1.5}{0.04}
\]

Calculating the right side:

\[
x = -37.5
\]

So, the value of \( x \) is:

\[
\boxed{-37.5}
\]