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dybincka [34]
3 years ago
8

Determine whether each expression is equivalent to

Mathematics
1 answer:
larisa [96]3 years ago
5 0

The algebraic expressions, x + x + y + y + y + y - 5 + x + x + x + 8 - 4y and 5x + 3 are equivalent to 2x + 4y - 5 + 3x + 8 - 4y

To determine whether each expression is equivalent to 2x + 4y - 5 + 3x + 8 - 4y, apply the knowledge of algebra to solve each of the following in it's simplest form.

First, simplify 2x + 4y - 5 + 3x + 8 - 4y as follows:

Add like terms

2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y - 5 + 8\\5x + 3

Next, compare or simplify where necessary each of the given algebraic expressions with 5x + 3

<em><u>First Option</u></em>

x + x + y + y + y + y - 5 + x + x + x + 8 - 4y

Add like terms together

2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y -5+8\\5x + 3

Therefore, x + x + y + y + y + y - 5 + x + x + x + 8 - 4y is equivalent to 2x + 4y - 5 + 3x + 8 - 4y

  • <em><u>Check the box for </u></em><em><u>YES.</u></em>

<u><em>Second Option:</em></u>

<u><em /></u>6xy + 3 - 4y<em> (cannot be simplified further)</em>

<em />6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y<em />

Therefore:

  • <em><u>Leave the box BLANK for </u></em><em><u>NO.</u></em>

<em><u /></em>

<em><u>Third Option:</u></em>

<em><u /></em>-8y + 5x - 3<em><u> </u></em><em>(cannot be simplified further)</em>

<em />-8y + 5x - 3 \neq  2x + 4y -5 + 3x + 8 - 4y<em />

Therefore:

  • <em><u>Leave the box BLANK for </u></em><em><u>NO.</u></em>

<em><u /></em>

<u><em>Fourth Option:</em></u>

<u><em /></u>5x + 3<u><em /></u>

<u><em /></u>5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y<u><em /></u>

Therefore:

  • <em><u>Check the box for </u></em><em><u>YES.</u></em>

<em><u></u></em>

Thus, the algebraic expressions that are equivalent to  2x + 4y - 5 + 3x + 8 - 4y are:

  • x + x + y + y + y + y - 5 + x + x + x + 8 - 4y
  • 5x + 3

Learn more about algebraic expressions here:

brainly.com/question/15122459

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