What is the solution to the equation: 3(x + 4) = 21?

What is the solution to the equation: 3(x + 4) = 21?

• A. x = 1
• B. x = 2
• C. x = 3
• D. x = 4

Answer: (C)

To solve the equation 3(x + 4) = 21, we start by isolating the expression inside the parentheses. First, we divide both sides of the equation by 3: \[ x + 4 = \frac{21}{3} \] This simplifies to: \[ x + 4 = 7 \] Next, we need to isolate x. We do this by subtracting 4 from both sides of the equation: \[ x = 7 - 4 \] This simplifies to: \[ x = 3 \] Thus, the solution to the equation is x = 3. Understanding why this solution is correct involves recognizing the steps taken to manipulate the equation properly. We divided by 3 to eliminate the coefficient of the expression and then subtracted the constant term to isolate x, ensuring we followed the correct order of operations. Consequently, the value of x that satisfies the original equation is indeed 3, confirming that option C is the correct answer.

To solve the equation 3(x + 4) = 21, we start by isolating the expression inside the parentheses. First, we divide both sides of the equation by 3:

[ x + 4 = \frac{21}{3} ]

This simplifies to:

[ x + 4 = 7 ]

Next, we need to isolate x. We do this by subtracting 4 from both sides of the equation:

[ x = 7 - 4 ]

This simplifies to:

[ x = 3 ]

Thus, the solution to the equation is x = 3.

Understanding why this solution is correct involves recognizing the steps taken to manipulate the equation properly. We divided by 3 to eliminate the coefficient of the expression and then subtracted the constant term to isolate x, ensuring we followed the correct order of operations. Consequently, the value of x that satisfies the original equation is indeed 3, confirming that option C is the correct answer.