Solve: `3(x+2)-2(x-1)=7`. Check the result.

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:

\[ 3(x + 2) - 2(x - 1) = 7 \]

Distributing \(3\) and \(-2\):

\[ 3x + 6 - 2x + 2 = 7 \]

### 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 need to isolate \(x\) by subtracting \(8\) from both sides:

\[ x = 7 - 8 \]

This gives us:

\[ x = -1 \]

### Step 4: Check the result
To verify our solution, we substitute \(x = -1\) back into the original equation:

\[ 3(-1 + 2) - 2(-1 - 1) = 7 \]

Calculating inside the parentheses first:

\[ 3(1) - 2(-2) = 7 \]

Now, simplify:

\[ 3 - (-4) = 7 \]

This simplifies to:

\[ 3 + 4 = 7 \]

Thus:

\[ 7 = 7 \]

Since both sides are equal, our solution is verified.

### Final Answer:
The solution to the equation is \(x = -1\).

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