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Answer :
To solve the expression [tex]\(30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right)\)[/tex], let's break it down step by step.
1. Distribute the constants in each part of the expression:
- For the first part, [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex]:
- Distribute 30 into the expression:
[tex]\[
30 \times \frac{1}{2} x = 15x
\][/tex]
[tex]\[
30 \times 2 = 60
\][/tex]
- So, [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex] becomes [tex]\(15x - 60\)[/tex].
- For the second part, [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex]:
- Distribute 40 into the expression:
[tex]\[
40 \times \frac{3}{4} y = 30y
\][/tex]
[tex]\[
40 \times 4 = 160
\][/tex]
- So, [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex] becomes [tex]\(30y - 160\)[/tex].
2. Combine the results from each part:
After distributing, combine the expressions:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
3. Simplify the combined expression:
Combine like terms:
[tex]\[
15x + 30y - 220
\][/tex]
The expression is simplified to [tex]\(15x + 30y - 220\)[/tex]. This matches one of the given options:
- [tex]\( 15x + 30y - 220 \)[/tex]
Therefore, the expression is equivalent to this option.
1. Distribute the constants in each part of the expression:
- For the first part, [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex]:
- Distribute 30 into the expression:
[tex]\[
30 \times \frac{1}{2} x = 15x
\][/tex]
[tex]\[
30 \times 2 = 60
\][/tex]
- So, [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex] becomes [tex]\(15x - 60\)[/tex].
- For the second part, [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex]:
- Distribute 40 into the expression:
[tex]\[
40 \times \frac{3}{4} y = 30y
\][/tex]
[tex]\[
40 \times 4 = 160
\][/tex]
- So, [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex] becomes [tex]\(30y - 160\)[/tex].
2. Combine the results from each part:
After distributing, combine the expressions:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
3. Simplify the combined expression:
Combine like terms:
[tex]\[
15x + 30y - 220
\][/tex]
The expression is simplified to [tex]\(15x + 30y - 220\)[/tex]. This matches one of the given options:
- [tex]\( 15x + 30y - 220 \)[/tex]
Therefore, the expression is equivalent to this option.
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