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------------------------------------------------ Which expression is equivalent to [tex]$30\left(\frac{1}{2} x-2\right)+40\left(\frac{3}{4} y-4\right)$[/tex]?

A. [tex]45xy - 220[/tex]
B. [tex]15x - 30y - 220[/tex]
C. [tex]15x + 30y - 220[/tex]
D. [tex]15x + 30y - 64[/tex]

Answer :

Let's solve the expression step-by-step:

The given expression is:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]

First, let's distribute [tex]\(30\)[/tex] in the first part:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) \][/tex]
[tex]\[ = 30 \cdot \frac{1}{2} x - 30 \cdot 2 \][/tex]
[tex]\[ = 15x - 60 \][/tex]

Next, let's distribute [tex]\(40\)[/tex] in the second part:
[tex]\[ 40\left(\frac{3}{4} y - 4\right) \][/tex]
[tex]\[ = 40 \cdot \frac{3}{4} y - 40 \cdot 4 \][/tex]
[tex]\[ = 30y - 160 \][/tex]

Now, let's combine both parts:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]

Combine the constants:
[tex]\[ = 15x + 30y - 220 \][/tex]

So, the expression simplifies to:
[tex]\[ 15x + 30y - 220 \][/tex]

The equivalent expression is [tex]\(15x + 30y - 220\)[/tex], which matches one of the answer choices. Therefore, the correct answer is:
[tex]\[ 15 x + 30 y - 220 \][/tex]