Answer :
Let's solve the expression step-by-step:
The given expression is:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
First, let's distribute [tex]\(30\)[/tex] in the first part:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) \][/tex]
[tex]\[ = 30 \cdot \frac{1}{2} x - 30 \cdot 2 \][/tex]
[tex]\[ = 15x - 60 \][/tex]
Next, let's distribute [tex]\(40\)[/tex] in the second part:
[tex]\[ 40\left(\frac{3}{4} y - 4\right) \][/tex]
[tex]\[ = 40 \cdot \frac{3}{4} y - 40 \cdot 4 \][/tex]
[tex]\[ = 30y - 160 \][/tex]
Now, let's combine both parts:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
Combine the constants:
[tex]\[ = 15x + 30y - 220 \][/tex]
So, the expression simplifies to:
[tex]\[ 15x + 30y - 220 \][/tex]
The equivalent expression is [tex]\(15x + 30y - 220\)[/tex], which matches one of the answer choices. Therefore, the correct answer is:
[tex]\[ 15 x + 30 y - 220 \][/tex]
The given expression is:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
First, let's distribute [tex]\(30\)[/tex] in the first part:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) \][/tex]
[tex]\[ = 30 \cdot \frac{1}{2} x - 30 \cdot 2 \][/tex]
[tex]\[ = 15x - 60 \][/tex]
Next, let's distribute [tex]\(40\)[/tex] in the second part:
[tex]\[ 40\left(\frac{3}{4} y - 4\right) \][/tex]
[tex]\[ = 40 \cdot \frac{3}{4} y - 40 \cdot 4 \][/tex]
[tex]\[ = 30y - 160 \][/tex]
Now, let's combine both parts:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
Combine the constants:
[tex]\[ = 15x + 30y - 220 \][/tex]
So, the expression simplifies to:
[tex]\[ 15x + 30y - 220 \][/tex]
The equivalent expression is [tex]\(15x + 30y - 220\)[/tex], which matches one of the answer choices. Therefore, the correct answer is:
[tex]\[ 15 x + 30 y - 220 \][/tex]
