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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]

Sure! Let's solve the expression step by step.

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

1. Distribute the multiplication in the first part:

- First, distribute the 30 to each term inside the parentheses:

[tex]\[ 30 \times \frac{1}{2}x = 15x \][/tex]
[tex]\[ 30 \times -2 = -60 \][/tex]

So, the expression becomes [tex]\( 15x - 60 \)[/tex].

2. Distribute the multiplication in the second part:

- Now, distribute the 40 to each term inside the parentheses:

[tex]\[ 40 \times \frac{3}{4}y = 30y \][/tex]
[tex]\[ 40 \times -4 = -160 \][/tex]

So, the expression becomes [tex]\( 30y - 160 \)[/tex].

3. Combine the simplified expressions:

Now, add the two parts together:

[tex]\[ 15x - 60 + 30y - 160 \][/tex]

4. Simplify the expression:

Combine the like terms:

- The coefficients of [tex]\( x \)[/tex] give us: [tex]\( 15x \)[/tex]
- The coefficients of [tex]\( y \)[/tex] give us: [tex]\( 30y \)[/tex]
- The constant terms: [tex]\( -60 - 160 = -220 \)[/tex]

Thus, the final simplified expression is:
[tex]\[ 15x + 30y - 220 \][/tex]

This matches the option: 15x + 30y - 220.