Sure, let's solve this step-by-step using the distributive property:
Given equation:
[tex]\[ 10 - 2(k + 4) = 3k - 8 \][/tex]
First, we distribute the [tex]\(-2\)[/tex] to both terms inside the parentheses:
[tex]\[ 10 - 2(k + 4) \][/tex]
[tex]\[ = 10 + (-2 \cdot k) + (-2 \cdot 4) \][/tex]
[tex]\[ = 10 - 2k - 8 \][/tex]
Now, simplify by combining the constant terms:
[tex]\[ = (10 - 8) - 2k \][/tex]
[tex]\[ = 2 - 2k \][/tex]
So we have:
[tex]\[ 2 - 2k = 3k - 8 \][/tex]
To express this in the form [tex]\(10 + \square + \diamond = 3k - 8\)[/tex]:
[tex]\[ 10 + (-2k - 8) = 3k - 8 \][/tex]
Let's break it down further. Since we distributed [tex]\(-2\)[/tex], we have two parts of the distribution:
[tex]\[10 + (-2 \cdot k) + (-2 \cdot 4) = 10 - 2k - 8\][/tex]
Therefore, the box (square) and question mark should be filled with [tex]\(-2k\)[/tex] and [tex]\(-8\)[/tex] respectively:
[tex]\[ 10 + (-2k - 8) = 3k - 8 \][/tex]
So, rewriting your expression step by step:
[tex]\[
\begin{array}{c}
10 - 2(k + 4) = 3k - 8 \\
10 + (-2k + -8) = 3k - 8 \\
10 + \square + \diamond = 3k - 8
\end{array}
\][/tex]
Where [tex]\(\square\)[/tex] is [tex]\(-2k\)[/tex] and [tex]\(\diamond\)[/tex] is [tex]\(-8\)[/tex].
Let's summarize the final expression:
[tex]\[ 10 + (-2k) + (-8) = 3k - 8 \][/tex]
So,
[tex]\[ 10 + (-2k) + (-8) = 3k - 8 \][/tex]
