Question

What would be the equation become after completing the first step from the Solving Equations Decision Chart?

4 + 2(1 + x) = 12

(The first question in the chart would be Are there any fractions or Decimals to remove? and multiplying them, but since we don't have any fractions/decimals we move on to the next question: Does the distributive property need to be used?)

Answer 1

After completing the first step of applying the distributive property to the equation \( 4 + 2(1 + x) = 12 \), we need to distribute the \( 2 \) across the terms in the parentheses.

Let's perform the distribution:

\[
2(1 + x) = 2 \cdot 1 + 2 \cdot x = 2 + 2x
\]

Now substituting this back into the equation gives us:

\[
4 + 2 + 2x = 12
\]

Now, combine the constants on the left side:

\[
6 + 2x = 12
\]

So, after completing the first step using the distributive property, the equation becomes:

\[
6 + 2x = 12
\]