Answer :
Let's simplify the expression step-by-step:
We start with the expression:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
1. Distribute the 30 in the first part of the expression:
[tex]\[
30\left(\frac{1}{2} x - 2\right) = 30 \times \frac{1}{2} \times x - 30 \times 2
\][/tex]
Simplify:
[tex]\[
15x - 60
\][/tex]
2. Distribute the 40 in the second part of the expression:
[tex]\[
40\left(\frac{3}{4} y - 4\right) = 40 \times \frac{3}{4} \times y - 40 \times 4
\][/tex]
Simplify:
[tex]\[
30y - 160
\][/tex]
3. Combine the results:
Combine the terms from both parts:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
4. Combine like terms:
Combine the constant terms:
[tex]\[
(15x + 30y) + (-60 - 160)
\][/tex]
This simplifies to:
[tex]\[
15x + 30y - 220
\][/tex]
So, the expression equivalent to the given one is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
The correct choice from the options is [tex]\( 15x + 30y - 220 \)[/tex], which matches:
- [tex]\( 15x + 30y - 220 \)[/tex]
We start with the expression:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
1. Distribute the 30 in the first part of the expression:
[tex]\[
30\left(\frac{1}{2} x - 2\right) = 30 \times \frac{1}{2} \times x - 30 \times 2
\][/tex]
Simplify:
[tex]\[
15x - 60
\][/tex]
2. Distribute the 40 in the second part of the expression:
[tex]\[
40\left(\frac{3}{4} y - 4\right) = 40 \times \frac{3}{4} \times y - 40 \times 4
\][/tex]
Simplify:
[tex]\[
30y - 160
\][/tex]
3. Combine the results:
Combine the terms from both parts:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
4. Combine like terms:
Combine the constant terms:
[tex]\[
(15x + 30y) + (-60 - 160)
\][/tex]
This simplifies to:
[tex]\[
15x + 30y - 220
\][/tex]
So, the expression equivalent to the given one is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
The correct choice from the options is [tex]\( 15x + 30y - 220 \)[/tex], which matches:
- [tex]\( 15x + 30y - 220 \)[/tex]
