Sure! Let's simplify the given expression using the distributive property step by step.
The given expression is:
[tex]\[
\frac{1}{2}(14d + 6t)
\][/tex]
Step 1: Recognize the distributive property which states [tex]\( a(b + c) = ab + ac \)[/tex]. In this case, [tex]\( a = \frac{1}{2} \)[/tex], [tex]\( b = 14d \)[/tex], and [tex]\( c = 6t \)[/tex].
Step 2: Distribute [tex]\(\frac{1}{2}\)[/tex] to both terms inside the parentheses:
[tex]\[
\frac{1}{2} \cdot 14d + \frac{1}{2} \cdot 6t
\][/tex]
Step 3: Simplify each term:
[tex]\[
\frac{1}{2} \cdot 14d = 7d
\][/tex]
[tex]\[
\frac{1}{2} \cdot 6t = 3t
\][/tex]
So, the expression simplifies to:
[tex]\[
7d + 3t
\][/tex]
Therefore, the result is:
[tex]\[
\frac{1}{2}(14d + 6t) = 7d + 3t
\][/tex]
