Answered

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Determine whether each expression is equivalent to

2x + 4y – 5 + 3x + 8 – 4y.

Check the box for Yes and leave blank for No.

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


6xy + 3 - 4y


-8y + 5x - 3


5x + 3

Sagot :

akposevictor

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

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

First, simplify [tex]2x + 4y - 5 + 3x + 8 - 4y[/tex] as follows:

Add like terms

[tex]2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y - 5 + 8\\5x + 3[/tex]

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

First Option

[tex]x + x + y + y + y + y - 5 + x + x + x + 8 - 4y[/tex]

Add like terms together

[tex]2x + 4y - 5 + 3x + 8 - 4y\\2x + 3x + 4y - 4y -5+8\\5x + 3[/tex]

Therefore, [tex]x + x + y + y + y + y - 5 + x + x + x + 8 - 4y[/tex] is equivalent to [tex]2x + 4y - 5 + 3x + 8 - 4y[/tex]

  • Check the box for YES.

Second Option:

[tex]6xy + 3 - 4y[/tex] (cannot be simplified further)

[tex]6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y[/tex]

Therefore:

  • Leave the box BLANK for NO.

Third Option:

[tex]-8y + 5x - 3[/tex] (cannot be simplified further)

[tex]-8y + 5x - 3 \neq 2x + 4y -5 + 3x + 8 - 4y[/tex]

Therefore:

  • Leave the box BLANK for NO.

Fourth Option:

[tex]5x + 3[/tex]

[tex]5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y[/tex]

Therefore:

  • Check the box for YES.

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

  • [tex]x + x + y + y + y + y - 5 + x + x + x + 8 - 4y[/tex]
  • [tex]5x + 3[/tex]

Learn more about algebraic expressions here:

https://brainly.com/question/15122459

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