To solve the equation \( 4y - 7 + 2y = -3(y - 1) - 1 \), we first simplify both sides step by step.
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Combine like terms on the left side: \[ (4y + 2y) - 7 = 6y - 7 \] Therefore, the left side becomes \( 6y - 7 \).
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Expand the right side: \[ -3(y - 1) - 1 = -3y + 3 - 1 = -3y + 2 \] Therefore, the right side simplifies to \( -3y + 2 \).
Now, we rewrite the equation with the simplified expressions: \[ 6y - 7 = -3y + 2 \]
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To isolate \( y \), first add \( 3y \) to both sides: \[ 6y + 3y - 7 = 2 \] This simplifies to: \[ 9y - 7 = 2 \]
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Next, add \( 7 \) to both sides: \[ 9y = 2 + 7 \] Simplifying gives: \[ 9y = 9 \]
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Finally, divide both sides by \( 9 \): \[ y = 1 \]
Thus, the solution to the equation is: \[ \boxed{1} \]
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