Solve the following.
`3(x+2)-2(x-1)=7`

Answer

To solve the equation \( 3(x + 2) - 2(x - 1) = 7 \), we will follow these steps:

### Step 1: Distribute the terms
We start by distributing the numbers outside the parentheses to the terms inside:
\[ 3(x + 2) = 3x + 6 \]
\[ -2(x - 1) = -2x + 2 \]
So, the equation becomes:
\[ 3x + 6 - 2x + 2 = 7 \]

### Step 2: Combine like terms
Next, we combine the like terms on the left side of the equation:
\[ (3x - 2x) + (6 + 2) = 7 \]
This simplifies to:
\[ x + 8 = 7 \]

### Step 3: Isolate the variable
Now, we want to isolate \( x \). We do this by moving the constant term (8) to the right side of the equation. To do this, we subtract 8 from both sides:
\[ x + 8 - 8 = 7 - 8 \]
This simplifies to:
\[ x = -1 \]

### Final Answer
Thus, the solution to the equation is:
\[ x = -1 \]

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