College

We appreciate your visit to Which expression is equivalent to tex 30 left frac 1 2 x 2 right 40 left frac 3 4 y 4 right tex A tex. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

Which expression is equivalent to [tex]$30\left(\frac{1}{2} x-2\right)+40\left(\frac{3}{4} y-4\right)$[/tex]?

A. [tex]45xy - 220[/tex]
B. [tex]15x - 30y - 220[/tex]
C. [tex]15x + 30y - 220[/tex]
D. [tex]15x + 30y - 64[/tex]

Answer :

Let's break down the given expression step by step:

The expression to simplify is:
[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]

1. Distribute the numbers inside the parentheses:
- For [tex]\( 30\left(\frac{1}{2} x - 2\right) \)[/tex]:
[tex]\[
30 \cdot \frac{1}{2} x - 30 \cdot 2 = 15x - 60
\][/tex]

- For [tex]\( 40\left(\frac{3}{4} y - 4\right) \)[/tex]:
[tex]\[
40 \cdot \frac{3}{4} y - 40 \cdot 4 = 30y - 160
\][/tex]

2. Combine the terms:
[tex]\[
15x - 60 + 30y - 160
\][/tex]

3. Simplify by combining like terms:
[tex]\[
15x + 30y - 220
\][/tex]

So, the equivalent expression is:
[tex]\[ 15x + 30y - 220 \][/tex]

Upon comparing with the given options:
- [tex]\( 45xy - 220 \)[/tex]
- [tex]\( 15x - 30y - 220 \)[/tex]
- [tex]\( 15x + 30y - 220 \)[/tex]
- [tex]\( 15x + 30y - 64 \)[/tex]

The correct answer is:
[tex]\[ 15x + 30y - 220 \][/tex]

Thanks for taking the time to read Which expression is equivalent to tex 30 left frac 1 2 x 2 right 40 left frac 3 4 y 4 right tex A tex. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada