High School

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 simplify the expression step-by-step:

We start with the expression:

[tex]\[ 30\left(\frac{1}{2} x - 2\right) + 40\left(\frac{3}{4} y - 4\right) \][/tex]

1. Distribute the 30 in the first part of the expression:

[tex]\[
30\left(\frac{1}{2} x - 2\right) = 30 \times \frac{1}{2} \times x - 30 \times 2
\][/tex]

Simplify:

[tex]\[
15x - 60
\][/tex]

2. Distribute the 40 in the second part of the expression:

[tex]\[
40\left(\frac{3}{4} y - 4\right) = 40 \times \frac{3}{4} \times y - 40 \times 4
\][/tex]

Simplify:

[tex]\[
30y - 160
\][/tex]

3. Combine the results:

Combine the terms from both parts:

[tex]\[
15x - 60 + 30y - 160
\][/tex]

4. Combine like terms:

Combine the constant terms:

[tex]\[
(15x + 30y) + (-60 - 160)
\][/tex]

This simplifies to:

[tex]\[
15x + 30y - 220
\][/tex]

So, the expression equivalent to the given one is:

[tex]\[ \boxed{15x + 30y - 220} \][/tex]

The correct choice from the options is [tex]\( 15x + 30y - 220 \)[/tex], which matches:

- [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