Bot GPT 4-o mini To solve the equation \( 0.5x - 0.3(0.2x + 5) = 0.4x - 3 \), we will first simplify the left side of the equation.
- 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:
\[ 0.5x - 0.06x - 1.5 = 0.4x - 3 \]
- Combine like terms on the left side:
\[ (0.5x - 0.06x) - 1.5 = 0.4x - 3 \]
\[ 0.44x - 1.5 = 0.4x - 3 \]
- 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:
\[ 0.44x - 0.4x - 1.5 = -3 \]
\[ 0.04x - 1.5 = -3 \]
- Now, add \( 1.5 \) to both sides:
\[ 0.04x = -3 + 1.5 \]
\[ 0.04x = -1.5 \]
- 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:
\[ \boxed{-37.5} \]
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