Answer :
To solve the expression [tex]\(30\left(\frac{1}{2} x-2\right)+40\left(\frac{3}{4} y-4\right)\)[/tex], we need to distribute and simplify each term carefully. Here's a step-by-step explanation:
1. Distribute the 30 across the first parenthesis:
- [tex]\(30 \times \left(\frac{1}{2} x\right) = 15x\)[/tex]
- [tex]\(30 \times (-2) = -60\)[/tex]
So, the expression for the first part is [tex]\(15x - 60\)[/tex].
2. Distribute the 40 across the second parenthesis:
- [tex]\(40 \times \left(\frac{3}{4} y\right) = 30y\)[/tex]
- [tex]\(40 \times (-4) = -160\)[/tex]
So, the expression for the second part is [tex]\(30y - 160\)[/tex].
3. Combine all the terms:
Now add the results from the two distributed expressions:
- [tex]\(15x - 60 + 30y - 160\)[/tex]
4. Simplify the combined expression:
Combine like terms:
- The coefficients: [tex]\(15x + 30y\)[/tex]
- The constants: [tex]\(-60 - 160 = -220\)[/tex]
The final simplified expression is [tex]\(15x + 30y - 220\)[/tex].
Now, comparing with the given choices:
- [tex]\(15x - 30y - 220\)[/tex]
- [tex]\(15x + 30y - 64\)[/tex]
- [tex]\(45xy - 220\)[/tex]
- [tex]\(15x + 30y - 220\)[/tex]
The correct equivalent expression is [tex]\(15x + 30y - 220\)[/tex].
1. Distribute the 30 across the first parenthesis:
- [tex]\(30 \times \left(\frac{1}{2} x\right) = 15x\)[/tex]
- [tex]\(30 \times (-2) = -60\)[/tex]
So, the expression for the first part is [tex]\(15x - 60\)[/tex].
2. Distribute the 40 across the second parenthesis:
- [tex]\(40 \times \left(\frac{3}{4} y\right) = 30y\)[/tex]
- [tex]\(40 \times (-4) = -160\)[/tex]
So, the expression for the second part is [tex]\(30y - 160\)[/tex].
3. Combine all the terms:
Now add the results from the two distributed expressions:
- [tex]\(15x - 60 + 30y - 160\)[/tex]
4. Simplify the combined expression:
Combine like terms:
- The coefficients: [tex]\(15x + 30y\)[/tex]
- The constants: [tex]\(-60 - 160 = -220\)[/tex]
The final simplified expression is [tex]\(15x + 30y - 220\)[/tex].
Now, comparing with the given choices:
- [tex]\(15x - 30y - 220\)[/tex]
- [tex]\(15x + 30y - 64\)[/tex]
- [tex]\(45xy - 220\)[/tex]
- [tex]\(15x + 30y - 220\)[/tex]
The correct equivalent expression is [tex]\(15x + 30y - 220\)[/tex].