Certainly! Let's consider the expression [tex]\((3 x)(4+y)-2.5 x\)[/tex] and simplify it step by step.
First, we distribute [tex]\( 3x \)[/tex] to both terms inside the parentheses:
[tex]\[
(3 x)(4 + y) - 2.5 x = 3x \cdot 4 + 3x \cdot y - 2.5x
\][/tex]
Next, we perform the multiplication for each term:
[tex]\[
3x \cdot 4 = 12x
\][/tex]
[tex]\[
3x \cdot y = 3xy
\][/tex]
So the expression now becomes:
[tex]\[
12x + 3xy - 2.5x
\][/tex]
Finally, we combine the like terms [tex]\(12x\)[/tex] and [tex]\(-2.5x\)[/tex]:
[tex]\[
12x - 2.5x = 9.5x
\][/tex]
So, the simplified expression is:
[tex]\[
9.5x + 3xy
\][/tex]
Therefore, the expression [tex]\((3 x)(4+y)-2.5 x\)[/tex] simplifies to [tex]\(9.5 x + 3 xy\)[/tex]. The correct answer is:
C) [tex]\(9.5 x + 3 xy\)[/tex]
