Question

3(4x+4)=2x+____+x+_____

Answer 1

To solve the equation \( 3(4x+4) = 2x + \_\_ + x + \_\_ \), we first simplify the left-hand side.

1. Distribute the 3 on the left side:
\[
3(4x+4) = 12x + 12
\]

Now, we rewrite the right side to show that it should ideally equal \( 12x + 12 \):
\[
2x + \_\_ + x + \_\_ = 12x + 12
\]

2. Combine the terms on the right side:
\[
2x + x = 3x
\]

Thus, the equation becomes:
\[
3x + \_\_ + \_\_ = 12x + 12
\]

3. To isolate the blanks, let's set up the equation:
\[
\_\_ + \_\_ = 12x + 12 - 3x = 9x + 12
\]

Let's say each blank is represented by \( a \) and \( b \):
\[
a + b = 9x + 12
\]

To express \( a \) and \( b \) in terms of \( x \), we need to choose values such that:
1. They combine to equal \( 9x + 12 \).
2. A simple choice could be:
- Set \( a = 9x \) and \( b = 12 \).

Therefore:
\[
2x + 9x + x + 12 = 12x + 12
\]

Summarizing:
\[
3(4x+4) = 2x + 9x + x + 12
\]
Thus, the blanks are \( 9x \) and \( 12 \).

In conclusion:
\[
\underline{9x} \quad \text{and} \quad \underline{12}
\]