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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 apply the distributive property to both parts of the expression, simplify, and then combine the results.
1. Distribute the 30:
- Consider the term [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex].
- Distribute the 30 to each part inside the parentheses:
- [tex]\(30 \times \frac{1}{2} x = 15x\)[/tex]
- [tex]\(30 \times -2 = -60\)[/tex]
- This yields: [tex]\(15x - 60\)[/tex].
2. Distribute the 40:
- Consider the term [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex].
- Distribute the 40 to each part inside the parentheses:
- [tex]\(40 \times \frac{3}{4} y = 30y\)[/tex]
- [tex]\(40 \times -4 = -160\)[/tex]
- This yields: [tex]\(30y - 160\)[/tex].
3. Combine the results:
- Now, add the expressions from the two distributed results:
- [tex]\((15x - 60) + (30y - 160)\)[/tex]
- Combine like terms:
- [tex]\(15x\)[/tex] is already simplified.
- [tex]\(30y\)[/tex] is already simplified.
- Combine constants: [tex]\(-60 - 160 = -220\)[/tex].
So, the simplified expression is [tex]\(15x + 30y - 220\)[/tex].
Thus, the expression equivalent to the original is [tex]\(15x + 30y - 220\)[/tex].
The correct answer is: [tex]\(15x + 30y - 220\)[/tex].
1. Distribute the 30:
- Consider the term [tex]\(30\left(\frac{1}{2} x - 2\right)\)[/tex].
- Distribute the 30 to each part inside the parentheses:
- [tex]\(30 \times \frac{1}{2} x = 15x\)[/tex]
- [tex]\(30 \times -2 = -60\)[/tex]
- This yields: [tex]\(15x - 60\)[/tex].
2. Distribute the 40:
- Consider the term [tex]\(40\left(\frac{3}{4} y - 4\right)\)[/tex].
- Distribute the 40 to each part inside the parentheses:
- [tex]\(40 \times \frac{3}{4} y = 30y\)[/tex]
- [tex]\(40 \times -4 = -160\)[/tex]
- This yields: [tex]\(30y - 160\)[/tex].
3. Combine the results:
- Now, add the expressions from the two distributed results:
- [tex]\((15x - 60) + (30y - 160)\)[/tex]
- Combine like terms:
- [tex]\(15x\)[/tex] is already simplified.
- [tex]\(30y\)[/tex] is already simplified.
- Combine constants: [tex]\(-60 - 160 = -220\)[/tex].
So, the simplified expression is [tex]\(15x + 30y - 220\)[/tex].
Thus, the expression equivalent to the original is [tex]\(15x + 30y - 220\)[/tex].
The correct answer is: [tex]\(15x + 30y - 220\)[/tex].
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