Bot GPT 4-o mini To solve the equation \( 0.5x - 0.3(0.2x + 5) = 0.4x - 3 \), we start by distributing the \( -0.3 \) on the left-hand side:
\[ 0.5x - 0.3(0.2x) - 0.3(5) = 0.4x - 3 \]
Calculating the distribution:
\[ 0.5x - 0.06x - 1.5 = 0.4x - 3 \]
Next, we combine the \( x \) terms on the left side:
\[ (0.5x - 0.06x) - 1.5 = 0.4x - 3 \]
This simplifies to:
\[ 0.44x - 1.5 = 0.4x - 3 \]
Next, we want to isolate the \( x \) terms by subtracting \( 0.4x \) from both sides:
\[ 0.44x - 0.4x - 1.5 = -3 \]
This simplifies to:
\[ 0.04x - 1.5 = -3 \]
Next, we add \( 1.5 \) to both sides:
\[ 0.04x = -3 + 1.5 \]
Calculating the right side:
\[ 0.04x = -1.5 \]
To solve for \( x \), we divide both sides by \( 0.04 \):
\[ x = \frac{-1.5}{0.04} \]
Calculating the division:
\[ x = -37.5 \]
Thus, the value of \( x \) is
\[ \boxed{-37.5} \]
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