Question

What is the value of x in the equation 0.2 + 0.4x - 0.3(x -10) = 0.3x - 4?

Answer 1

To solve the equation

\[
0.2 + 0.4x - 0.3(x - 10) = 0.3x - 4,
\]

we will first expand and simplify both sides.

Starting with the left-hand side, distribute \(-0.3\) across \((x - 10)\):

\[
0.2 + 0.4x - 0.3x + 3 = 0.3x - 4,
\]

where \( -0.3 \cdot -10 = 3\).

Now combine the constant terms and the \(x\) terms on the left:

\[
0.2 + 3 + 0.4x - 0.3x = 0.3x - 4.
\]

This simplifies to:

\[
3.2 + 0.1x = 0.3x - 4.
\]

Next, we'll move all terms involving \(x\) to one side and constant terms to the other. Subtract \(0.1x\) from both sides:

\[
3.2 = 0.3x - 0.1x - 4,
\]

which simplifies to:

\[
3.2 = 0.2x - 4.
\]

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

\[
3.2 + 4 = 0.2x,
\]

which gives:

\[
7.2 = 0.2x.
\]

Finally, solve for \(x\) by dividing both sides by \(0.2\):

\[
x = \frac{7.2}{0.2} = 36.
\]

Thus, the value of \(x\) is

\[
\boxed{36}.
\]