Solve: `x/2-1=x/3+4`

Options

A. `x=30`
B. `x=5`
C. `x=1`
D. `x=4`

Answer

To solve the equation \( \frac{x}{2} - 1 = \frac{x}{3} + 4 \), we will follow these steps:

### Step 1: Move all terms involving \( x \) to one side and constant terms to the other side.
We start with the equation:
\[ \frac{x}{2} - 1 = \frac{x}{3} + 4 \]
Add \( 1 \) to both sides:
\[ \frac{x}{2} = \frac{x}{3} + 4 + 1 \]
This simplifies to:
\[ \frac{x}{2} = \frac{x}{3} + 5 \]

### Step 2: Move \( \frac{x}{3} \) to the left side.
Subtract \( \frac{x}{3} \) from both sides:
\[ \frac{x}{2} - \frac{x}{3} = 5 \]

### Step 3: Find a common denominator for the fractions on the left side.
The least common multiple (LCM) of \( 2 \) and \( 3 \) is \( 6 \). Rewrite the fractions:
\[ \frac{3x}{6} - \frac{2x}{6} = 5 \]

### Step 4: Combine the fractions.
Now combine the fractions:
\[ \frac{3x - 2x}{6} = 5 \]
This simplifies to:
\[ \frac{x}{6} = 5 \]

### Step 5: Eliminate the fraction by multiplying both sides by \( 6 \).
Multiply both sides by \( 6 \):
\[ x = 5 \times 6 \]
This gives us:
\[ x = 30 \]

### Final Answer:
The solution to the equation is:
\[ \boxed{30} \]

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