Solve the following equations.Check your result in each case
`3x+2(x+2)=20-(2x-5)`

Options

A. `x=2`
B. `x=3`
C. `x=4`
D. `x=5`

Answer

To solve the equation \(3x + 2(x + 2) = 20 - (2x - 5)\), we will follow these steps:

### Step 1: Expand the equation
First, we will expand both sides of the equation.

On the left side:
\[ 2(x + 2) = 2x + 4 \]
So, the left side becomes:
\[ 3x + 2x + 4 \]

On the right side:
\[ 20 - (2x - 5) = 20 - 2x + 5 = 25 - 2x \]

Now, the equation looks like this:
\[ 3x + 2x + 4 = 25 - 2x \]

### Step 2: Combine like terms
Now, we combine the like terms on the left side:
\[ 5x + 4 = 25 - 2x \]

### Step 3: Move all terms involving \(x\) to one side
Next, we will add \(2x\) to both sides to get all \(x\) terms on the left:
\[ 5x + 2x + 4 = 25 \]
This simplifies to:
\[ 7x + 4 = 25 \]

### Step 4: Move constant terms to the other side
Now, we will subtract \(4\) from both sides:
\[ 7x = 25 - 4 \]
This simplifies to:
\[ 7x = 21 \]

### Step 5: Solve for \(x\)
Now, we divide both sides by \(7\):
\[ x = \frac{21}{7} = 3 \]

### Step 6: Check the result
To verify our solution, we will substitute \(x = 3\) back into the original equation:
\[ 3(3) + 2(3 + 2) = 20 - (2(3) - 5) \]
Calculating the left side:
\[ 9 + 2(5) = 9 + 10 = 19 \]
Calculating the right side:
\[ 20 - (6 - 5) = 20 - 1 = 19 \]
Since both sides are equal, our solution is confirmed.

### Final Answer
Thus, the solution to the equation is:
\[ x = 3 \]

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