Respuesta :
Answer: The correct answer choices are:
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[A]: " 0 + y " ; And:
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[B]: " y " .
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Step-by-step explanation:
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We have:
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The given expression:
" x - (-x) + y " .
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We are asked: "Which of the following expressions are equivalent to:
"x - (-x) + y " ; {i.e. the given expression.}. ? "
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We are given 3 (three answer choices):
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Choice [A]: " 0 + y " ;
Choice [B]: " y " ;
Choice [C]: "None of the above" .
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Now, let us take a look at our given expression:
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" x - (-x) + y " .
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Can this be simplified? Yes!
The " x - (-x) " can be reduced to : " x + x " ; which equals:
" 1x + 1x " ; which equals "2x" ;
and the "given expression" can be simplified to:
" 2x + y " .
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Note that: " x - (-x) " = " x + x " ;
because: a "negative" minus a "negative" equals a "positive" ;
that is; the "negative value" of a "negative value" is a "positive value".
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So we have:
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" 2x + y " ; as our "simplified" given expression.
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Now, given our 3 (three) answer choices; we are asked to choose all the answer choices that apply;
→ {i.e. ; {" Which of the 3 [three] answer choices are equal to the given expression; or, for that matter, our "simplified" given expression:
→ " x - (-x) + y " ; or; " 2x + y " } ?
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Let us start with the first answer choice given:
Choice [A]: " 0 + y " .
is: " 2x + y " ; equal to: "0 + y " ?
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Subtract "y" from each side of the equation:
2x + y - y = 0 + y - y ;
to get:
2x = 0 ;
Divide each side of the equation by "2" ;
2x / 2 = 0 / 2 ;
to get:
x = 0 .
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So, does: " 2x + y = 0 + y " ? ;
Answer: Yes! When: x = 0 ! ;
Let us check by plugging in "0" for "x" ;
" 2x + y =? 0 + y " ;
→ " 2(0) + y =? 0 + y ;
Note: " 2×0 = 0" .
→ " 0 + y =? 0 + y " ? Yes!
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Now, let us check with the "non-simplified" given expression:
" x - (-x) + y " ;
→ " x - (-x) + y = ? 0 + y " ? ;
Subtract "y" from each side of the equation;
→ " x - (-x) + y - y = ? 0 + y - y " ;
→ "x - (x) =? 0 " ? ;
→ " x - x = 0 " ? Yes! ; {" 1x - 1x = 0 ."}.
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So; Answer choice: [A]: " 0 + y " ; is a correct answer.
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Let us continue with the second answer choice given:
Choice [B]: " y " .
Is the simplified version of our given equation: " 2x + y " ;
equal to: "y " ?
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Does: " 2x + y =? y " ?
The answer is: Yes; because we have determined that:
Answer choice: [A]: " 0 + y " ; is correct; and:
Answer choice: [B]: " y " ; is equal to: " 0 + y " .
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As such: Answer choice: [B]: " y " ; is a correct answer.
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We can 'rule out" Answer choice: [C]: "none of the above" ; since both of the above given answer choices are correct.
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The correct answer choices are:
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[A]: " 0 + y " ; And:
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[B]: " y " .
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Hope this helps!
Wishing you the best in your academic pursuits
— and within the "Brainly" community!
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