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Answer :
Sure! Let's break down the expression step by step.
We need to simplify the given expression:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
Step 1: Distribute the numbers outside the parentheses.
1. For the first part, [tex]\( 30\left(\frac{1}{2} x - 2\right) \)[/tex]:
- 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 becomes [tex]\( 15x - 60 \)[/tex].
2. For the second part, [tex]\( 40\left(\frac{3}{4} y - 4\right) \)[/tex]:
- 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 becomes [tex]\( 30y - 160 \)[/tex].
Step 2: Combine the results from both distributions.
Combine the expressions from both parts:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
Combine the like terms:
- [tex]\( 15x \)[/tex] stays as it is.
- [tex]\( 30y \)[/tex] stays as it is.
- Combine the constants: [tex]\(-60 - 160 = -220\)[/tex]
So, the simplified expression is:
[tex]\[
15x + 30y - 220
\][/tex]
The expression equivalent to the given one is:
[tex]\[ 15x + 30y - 220 \][/tex]
Therefore, the correct answer is:
[tex]\[ \text{15}x + 30y - 220 \][/tex]
We need to simplify the given expression:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]
Step 1: Distribute the numbers outside the parentheses.
1. For the first part, [tex]\( 30\left(\frac{1}{2} x - 2\right) \)[/tex]:
- 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 becomes [tex]\( 15x - 60 \)[/tex].
2. For the second part, [tex]\( 40\left(\frac{3}{4} y - 4\right) \)[/tex]:
- 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 becomes [tex]\( 30y - 160 \)[/tex].
Step 2: Combine the results from both distributions.
Combine the expressions from both parts:
[tex]\[
15x - 60 + 30y - 160
\][/tex]
Combine the like terms:
- [tex]\( 15x \)[/tex] stays as it is.
- [tex]\( 30y \)[/tex] stays as it is.
- Combine the constants: [tex]\(-60 - 160 = -220\)[/tex]
So, the simplified expression is:
[tex]\[
15x + 30y - 220
\][/tex]
The expression equivalent to the given one is:
[tex]\[ 15x + 30y - 220 \][/tex]
Therefore, the correct answer is:
[tex]\[ \text{15}x + 30y - 220 \][/tex]
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