Solve for x:-`2(x+5)-(x-6)=3(x+7)-3`

Options

A. 1
B. -1
C. 2
D. 0

Answer

To solve the equation \(2(x+5)-(x-6)=3(x+7)-3\), we will follow these steps:

### Step 1: Expand both sides of the equation
We start by distributing the terms in the brackets.

Left-hand side:
\[ 2(x + 5) - (x - 6) = 2x + 10 - x + 6 \]

Right-hand side:
\[ 3(x + 7) - 3 = 3x + 21 - 3 \]

### Step 2: Simplify both sides
Now, we will simplify both sides of the equation.

Left-hand side:
\[ 2x + 10 - x + 6 = (2x - x) + (10 + 6) = x + 16 \]

Right-hand side:
\[ 3x + 21 - 3 = 3x + (21 - 3) = 3x + 18 \]

So, we have:
\[ x + 16 = 3x + 18 \]

### Step 3: Rearrange the equation
Next, we will move all terms involving \(x\) to one side and constant terms to the other side.

Subtract \(x\) from both sides:
\[ 16 = 3x - x + 18 \]
This simplifies to:
\[ 16 = 2x + 18 \]

### Step 4: Isolate \(x\)
Now, we will isolate \(x\) by subtracting 18 from both sides:
\[ 16 - 18 = 2x \]
This simplifies to:
\[ -2 = 2x \]

### Step 5: Solve for \(x\)
Finally, divide both sides by 2:
\[ x = \frac{-2}{2} = -1 \]

### Final Answer
Thus, the solution for \(x\) is:
\[ \boxed{-1} \]

---