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]
Second Option:
[tex]6xy + 3 - 4y[/tex] (cannot be simplified further)
[tex]6xy + 3 - 4y\neq 2x + 4y - 5 + 3x + 8 - 4y[/tex]
Therefore:
Third Option:
[tex]-8y + 5x - 3[/tex] (cannot be simplified further)
[tex]-8y + 5x - 3 \neq 2x + 4y -5 + 3x + 8 - 4y[/tex]
Therefore:
Fourth Option:
[tex]5x + 3[/tex]
[tex]5x + 3 = 2x + 4y - 5 + 3x + 8 - 4y[/tex]
Therefore:
Thus, the algebraic expressions that are equivalent to [tex]2x + 4y - 5 + 3x + 8 - 4y[/tex] are:
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