Answer :
Let's break down the given expression step by step:
The expression to simplify is:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
1. Distribute the numbers inside the parentheses:
- For [tex]\( 30\left(\frac{1}{2} x - 2\right) \)[/tex]:
[tex]\[
30 \cdot \frac{1}{2} x - 30 \cdot 2 = 15x - 60
\][/tex]
- For [tex]\( 40\left(\frac{3}{4} y - 4\right) \)[/tex]:
[tex]\[
40 \cdot \frac{3}{4} y - 40 \cdot 4 = 30y - 160
\][/tex]
2. Combine the terms:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
3. Simplify by combining like terms:
[tex]\[
15x + 30y - 220
\][/tex]
So, the equivalent expression is:
[tex]\[ 15x + 30y - 220 \][/tex]
Upon comparing with the given options:
- [tex]\( 45xy - 220 \)[/tex]
- [tex]\( 15x - 30y - 220 \)[/tex]
- [tex]\( 15x + 30y - 220 \)[/tex]
- [tex]\( 15x + 30y - 64 \)[/tex]
The correct answer is:
[tex]\[ 15x + 30y - 220 \][/tex]
The expression to simplify is:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
1. Distribute the numbers inside the parentheses:
- For [tex]\( 30\left(\frac{1}{2} x - 2\right) \)[/tex]:
[tex]\[
30 \cdot \frac{1}{2} x - 30 \cdot 2 = 15x - 60
\][/tex]
- For [tex]\( 40\left(\frac{3}{4} y - 4\right) \)[/tex]:
[tex]\[
40 \cdot \frac{3}{4} y - 40 \cdot 4 = 30y - 160
\][/tex]
2. Combine the terms:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
3. Simplify by combining like terms:
[tex]\[
15x + 30y - 220
\][/tex]
So, the equivalent expression is:
[tex]\[ 15x + 30y - 220 \][/tex]
Upon comparing with the given options:
- [tex]\( 45xy - 220 \)[/tex]
- [tex]\( 15x - 30y - 220 \)[/tex]
- [tex]\( 15x + 30y - 220 \)[/tex]
- [tex]\( 15x + 30y - 64 \)[/tex]
The correct answer is:
[tex]\[ 15x + 30y - 220 \][/tex]