Solve for x.
$\begin{array}{c}
3(2 x+4)=24 \\
x=[?]
\end{array}$
Answer (1)
Distribute the constant: 3 ( 2 x + 4 ) = 6 x + 12 .
Rewrite the equation: 6 x + 12 = 24 .
Subtract 12 from both sides: 6 x = 12 .
Divide by 6 to solve for x: x = 2 .
Explanation
Understanding the Problem We are given the equation 3 ( 2 x + 4 ) = 24 and we want to solve for x .
Distributing the Constant First, we distribute the 3 on the left side of the equation: 3 ( 2 x + 4 ) = 3 × 2 x + 3 × 4 = 6 x + 12 . So the equation becomes 6 x + 12 = 24 .
Isolating the x Term Next, we subtract 12 from both sides of the equation to isolate the term with x : 6 x + 12 − 12 = 24 − 12 , which simplifies to 6 x = 12 .
Solving for x Finally, we divide both sides of the equation by 6 to solve for x : 6 6 x = 6 12 , which simplifies to x = 2 .
Examples
Imagine you're planning a pizza party. You know that each pizza has 6 slices, and you want to figure out how many pizzas you need to buy so that each of your 12 guests can have at least 3 slices. This problem is similar to solving for x in an equation. By setting up an equation, you can determine the exact number of pizzas required to satisfy your guests' appetites. This kind of problem-solving helps in everyday situations where you need to allocate resources or plan quantities.
