To solve the equation \( 4x + 6 = 5x + 7 \), follow these steps:
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Subtract \( 4x \) from both sides:
\[ 6 = 5x - 4x + 7 \]
This simplifies to:
\[ 6 = x + 7 \]
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Next, subtract \( 7 \) from both sides:
\[ 6 - 7 = x \]
This simplifies to:
\[ -1 = x \]
So, the solution is:
\[ x = -1 \]