Bot GPT 4-o mini 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
\[ \boxed{36}. \]
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