To solve the equation \( x + 4x - 3 = 3x - 9 \), we can start by combining like terms.
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Combine the like terms on the left side: \[ 5x - 3 = 3x - 9 \]
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Next, we can isolate \( x \) by getting all terms with \( x \) on one side and constants on the other. Subtract \( 3x \) from both sides: \[ 5x - 3x - 3 = -9 \] This simplifies to: \[ 2x - 3 = -9 \]
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Now, add 3 to both sides to isolate \( 2x \): \[ 2x = -9 + 3 \] Simplifying further gives: \[ 2x = -6 \]
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Finally, divide both sides by 2: \[ x = -3 \]
Thus, the solution to the equation is: \[ \boxed{-3} \]