Answer: The correct answer is: " - 10 ".
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However, this answer, " -10 ", does not correspond to any of the answer choices given.
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Explanation:
Given: -9 −︱9 + (-3) + (-5)︱ ;
We are to simplify this expression by using the 'order of operations'—as follows:
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BE MD AS ; or: PE MD AS
⇒ ⇒ ⇒ ⇒
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which is a mnemonic device to remember the "order of operations":
Be Excused, My Dear Aunt Sally (Susan).
or: Please Excuse My Dear Aunt Sally (Susan).
Note: the "B" stands for "Brackets" ,
and the "P" stands for "Parentheses."
Note that "parentheses" can function as "brackets."
The "E" stands for "Exponents".
→ The "Brackets/Parentheses" —if they occur; take priority.
Then: MD for "Multiplication and Division" are the next priority;
⇒
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→ and that neither takes priority over the other. Take note of the " ⇒ " symbol" below the "MD". This means that we perform "multiplication and division"—as they occur, from the far left of ["beginning of"] the expression to the end of the expression.
Then: We do the same with "Addition and Subtraction"—from the beginning to the end of the expression, in that order [that is, from "left to right"—as/if they occur]—hence the "⇒" notation.
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So again, our given expression is:
" -9 −︱9 + (-3) + (-5)︱ " ;
So; we have an "absolute value" (the positive integer of what is enclosed within the "vertical lines" that indicate "absolute value"—or, if the value of what is enclosed within the "vertical lines" is "0" [zero], then the absolute value would be "0" [zero]; since the absolute value of 0 is 0.
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So, let's start simplifying by using the 'order of operations.'
Do we have brackets or parentheses? No; except for the absolute value lines — which do take priority. The parentheses within those lines do not count for our purposes—but if they did, then we would use the order of operations within the "absolute value" bars!
So as a matter of 'semantics', we could say: 'Yes"; that the absolute value bars function as "brackets."
Do we have any "exponent(s)"? No.
Is there any multiplication/division? No.
Do we have any addition or subtraction? Yes; only one:
→ " - 9 −︱9 + (-3) + (-5)︱.
→ {not including the addition and subtraction within the absolute value bars.}.
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Let's start by simplifying the expression within the absolute value bars:
︱9 + (-3) + (-5)︱;
Note: The only operations are additional and subtraction; so we just calculate from left to right; as these operations occur:
" 9 + (-3) " = 9 − 3 " ; Note: Adding a "negative value" is the same as subtracting a "possible value" ;
to get: " 6 " ;
Then: the next step is:
" 6 + (-5) " = 6 − 5 " ; Note:
Adding a "negative value" is the same as subtracting a "positive value" ;
to get: " 1 ".
Now, the absolute of " 1" is " 1".
→ or; write as: ︱1︱= 1 .
Now, we can rewrite the entire expression:
" - 9 − 1 " ; to calculate and simplify:
to get: " - 10 " .
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Hope this answer is correct and helpful!
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However, this answer, "-10", does not correspond to any of the given answer choices.
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Best wishes!
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