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Which of the following expressions is equivalent to [tex]$(3x)(4+y) - 2.5x$[/tex]?

A. [tex]12x - 0.5xy[/tex]

B. [tex]14.5x + 3y[/tex]

C. [tex]9.5x + 3xy[/tex]

D. [tex]7x - 2.5y[/tex]

Sagot :

GinnyAnsweridn
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]
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