The expression `7(x + 3) - 3(2x - 2)` is equivalent to :

Options

A. `x + 1`
B. `x + 15`
C. `x + 19`
D. `x + 27`

Answer

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

### Step 1: Distribute the terms
We start by distributing the terms in the expression.

\[ 7(x + 3) = 7 \cdot x + 7 \cdot 3 = 7x + 21 \]

\[ -3(2x - 2) = -3 \cdot 2x + (-3) \cdot (-2) = -6x + 6 \]

### Step 2: Combine the distributed terms
Now we combine the results from Step 1.

\[ 7x + 21 - 6x + 6 \]

### Step 3: Combine like terms
Next, we combine the like terms (the \(x\) terms and the constant terms).

For the \(x\) terms:
\[ 7x - 6x = 1x = x \]

For the constant terms:
\[ 21 + 6 = 27 \]

### Step 4: Write the final expression
Putting it all together, we have:

\[ x + 27 \]

Thus, the expression \( 7(x + 3) - 3(2x - 2) \) is equivalent to \( x + 27 \).

### Final Answer:
The expression is equivalent to \( x + 27 \).

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