Answer :
Sure! Let's go through the process of simplifying the expression step-by-step:
The problem asks us to find which expression is equivalent to:
[tex]\[ 30\left(\frac{1}{2} x-2\right) + 40\left(\frac{3}{4} y-4\right) \][/tex]
To do this, we'll distribute the numbers outside the parentheses to each term inside.
1. Distribute the 30 inside the first set of parentheses:
- Multiply [tex]\(30\)[/tex] by [tex]\(\frac{1}{2} x\)[/tex]:
[tex]\[ 30 \times \frac{1}{2} x = 15x \][/tex]
- Multiply [tex]\(30\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[ 30 \times (-2) = -60 \][/tex]
So the first part is [tex]\(15x - 60\)[/tex].
2. Distribute the 40 inside the second set of parentheses:
- Multiply [tex]\(40\)[/tex] by [tex]\(\frac{3}{4} y\)[/tex]:
[tex]\[ 40 \times \frac{3}{4} y = 30y \][/tex]
- Multiply [tex]\(40\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 40 \times (-4) = -160 \][/tex]
So the second part is [tex]\(30y - 160\)[/tex].
3. Combine both parts:
Add the two simplified parts together:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
4. Simplify further:
Combine the constant terms:
- [tex]\(-60 - 160 = -220\)[/tex]
Thus, the simplified expression is:
[tex]\[ 15x + 30y - 220 \][/tex]
Therefore, the expression equivalent to the original one given is:
[tex]\[ 15x + 30y - 220 \][/tex]
The correct option is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]
The problem asks us to find which expression is equivalent to:
[tex]\[ 30\left(\frac{1}{2} x-2\right) + 40\left(\frac{3}{4} y-4\right) \][/tex]
To do this, we'll distribute the numbers outside the parentheses to each term inside.
1. Distribute the 30 inside the first set of parentheses:
- Multiply [tex]\(30\)[/tex] by [tex]\(\frac{1}{2} x\)[/tex]:
[tex]\[ 30 \times \frac{1}{2} x = 15x \][/tex]
- Multiply [tex]\(30\)[/tex] by [tex]\(-2\)[/tex]:
[tex]\[ 30 \times (-2) = -60 \][/tex]
So the first part is [tex]\(15x - 60\)[/tex].
2. Distribute the 40 inside the second set of parentheses:
- Multiply [tex]\(40\)[/tex] by [tex]\(\frac{3}{4} y\)[/tex]:
[tex]\[ 40 \times \frac{3}{4} y = 30y \][/tex]
- Multiply [tex]\(40\)[/tex] by [tex]\(-4\)[/tex]:
[tex]\[ 40 \times (-4) = -160 \][/tex]
So the second part is [tex]\(30y - 160\)[/tex].
3. Combine both parts:
Add the two simplified parts together:
[tex]\[ 15x - 60 + 30y - 160 \][/tex]
4. Simplify further:
Combine the constant terms:
- [tex]\(-60 - 160 = -220\)[/tex]
Thus, the simplified expression is:
[tex]\[ 15x + 30y - 220 \][/tex]
Therefore, the expression equivalent to the original one given is:
[tex]\[ 15x + 30y - 220 \][/tex]
The correct option is:
[tex]\[ \boxed{15x + 30y - 220} \][/tex]