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Answer :
To find the expression that is equivalent to [tex]\(30\left(\frac{1}{2} x-2\right) + 40\left(\frac{3}{4} y-4\right)\)[/tex], we need to use the distributive property to simplify each part separately and then combine the results.
1. Simplify the first part:
[tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex]
- 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 for the first part is:
[tex]\(15x - 60\)[/tex]
2. Simplify the second part:
[tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex]
- 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 for the second part is:
[tex]\(30y - 160\)[/tex]
3. Combine the simplified expressions:
- Add the results from the first and second parts together:
[tex]\[
(15x - 60) + (30y - 160) = 15x + 30y - 220
\][/tex]
Therefore, the expression equivalent to [tex]\(30\left(\frac{1}{2} x-2\right) + 40\left(\frac{3}{4} y-4\right)\)[/tex] is [tex]\(15x + 30y - 220\)[/tex].
The correct answer is: [tex]\(\boxed{15x + 30y - 220}\)[/tex].
1. Simplify the first part:
[tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex]
- 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 for the first part is:
[tex]\(15x - 60\)[/tex]
2. Simplify the second part:
[tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex]
- 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 for the second part is:
[tex]\(30y - 160\)[/tex]
3. Combine the simplified expressions:
- Add the results from the first and second parts together:
[tex]\[
(15x - 60) + (30y - 160) = 15x + 30y - 220
\][/tex]
Therefore, the expression equivalent to [tex]\(30\left(\frac{1}{2} x-2\right) + 40\left(\frac{3}{4} y-4\right)\)[/tex] is [tex]\(15x + 30y - 220\)[/tex].
The correct answer is: [tex]\(\boxed{15x + 30y - 220}\)[/tex].
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