To solve the equation \( 2x - 7 = \frac{x}{2} - 1 \), follow these steps:
- Start by eliminating the fraction. To do this, multiply every term by 2 (the denominator):
\[ 2(2x - 7) = 2\left(\frac{x}{2} - 1\right) \]
This simplifies to:
\[ 4x - 14 = x - 2 \]
- Next, isolate \(x\) by getting all \(x\) terms on one side and constant terms on the other side. Subtract \(x\) from both sides:
\[ 4x - x - 14 = -2 \]
This simplifies to:
\[ 3x - 14 = -2 \]
- Now, add 14 to both sides:
\[ 3x = 12 \]
- Finally, divide both sides by 3 to solve for \(x\):
\[ x = 4 \]
Thus, the solution to the equation \( 2x - 7 = \frac{x}{2} - 1 \) is
\[ \boxed{4} \]
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