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. Expand each term inside the parentheses:
[tex]\[ 30 \left( \frac{1}{2} x - 2 \right) \quad \text{and} \quad 40 \left( \frac{3}{4} y - 4 \right) \][/tex]
2. Distribute the coefficients:
[tex]\[ 30 \left( \frac{1}{2} x \right) - 30 \cdot 2 \quad \text{and} \quad 40 \left( \frac{3}{4} y \right) - 40 \cdot 4 \][/tex]
3. Multiply the terms:
[tex]\[ 30 \cdot \frac{1}{2} x - 60 \quad \text{and} \quad 40 \cdot \frac{3}{4} y - 160 \][/tex]
4. Simplify the expressions:
[tex]\[ 15x - 60 \quad \text{and} \quad 30y - 160 \][/tex]
5. Combine like terms (constants) and put the expression together:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
6. Simplify by combining the constants:
[tex]\[ 15x + 30y - 220 \][/tex]
Thus, 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]
So, the correct answer is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
1. Expand each term inside the parentheses:
[tex]\[ 30 \left( \frac{1}{2} x - 2 \right) \quad \text{and} \quad 40 \left( \frac{3}{4} y - 4 \right) \][/tex]
2. Distribute the coefficients:
[tex]\[ 30 \left( \frac{1}{2} x \right) - 30 \cdot 2 \quad \text{and} \quad 40 \left( \frac{3}{4} y \right) - 40 \cdot 4 \][/tex]
3. Multiply the terms:
[tex]\[ 30 \cdot \frac{1}{2} x - 60 \quad \text{and} \quad 40 \cdot \frac{3}{4} y - 160 \][/tex]
4. Simplify the expressions:
[tex]\[ 15x - 60 \quad \text{and} \quad 30y - 160 \][/tex]
5. Combine like terms (constants) and put the expression together:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
6. Simplify by combining the constants:
[tex]\[ 15x + 30y - 220 \][/tex]
Thus, 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]
So, the correct answer is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
