To solve the equation \( 3x + 19 + 7x + 1 = -200 \), we first combine like terms on the left side.
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Combine the \( x \) terms: \[ 3x + 7x = 10x \]
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Combine the constant terms: \[ 19 + 1 = 20 \]
Now, we can rewrite the equation as: \[ 10x + 20 = -200 \]
Next, we want to isolate \( x \). First, subtract 20 from both sides: \[ 10x + 20 - 20 = -200 - 20 \] \[ 10x = -220 \]
Now, divide both sides by 10: \[ x = \frac{-220}{10} \] \[ x = -22 \]
Thus, the solution to the equation is: \[ \boxed{-22} \]