When solving negative one over eight (x + 35) = −7, what is the correct sequence of operations? (5 points)Multiply each side by negative one over eight , add 35 to each sideMultiply each side by negative one over eight , subtract 35 from each sideMultiply each side by −8, subtract 35 from each sideMultiply each side by −8, add 35 to each side

The correct answer choice is:  
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  [C]:  "Multiply each side by −8, subtract 35 from each side" .
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Explanation:
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Given:  "[tex] \frac{-1}{8} [/tex] (x + 35) = -7 " ; 

We can START by multiply each side of the equation by "-8"  to completely get rid of the "[tex] \frac{-1}{8} [/tex]"  fraction on the "left-hand-side" of the equation:

since:  "[tex] \frac{-1}{8} [/tex]  * -8 = 1 ;  and:  "1" , multiplied by any given value, is equal to that given value; so in effect, the "1" becomes eliminated.

" [tex] \frac{-1}{8} [/tex]  * -8 =  

[tex] \frac{-1}{8} [/tex] * [tex] \frac{-8}{1} [/tex] =


[tex] \frac{(-1*-8)}{(8* 1)} [/tex] = [tex] \frac{8}{8} [/tex] = 1 .
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So,  given:  "[tex] \frac{-1}{8} [/tex] (x + 35) = -7 " ; ; 

We multiply each side of the equation by "-8" ; 

→    -8 * { [tex] \frac{-1}{8} [/tex] (x + 35) }  =  -7 * {-8) " ; 

→    1 (x + 35)  = 56 ; 

     →  x + 35 = 56 ;

Then, we SUBTRACT "35" (FROM EACH SIDE OF THE EQUATION) ;  to isolate "x" on ONE SIDE OF THE EQUATION; and to solve for "x" ;

     →  x + 35 − 35 = 56 − 35 ;

     →  x = 21 .
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So, as explained, the correct answer is:  
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   Answer choice:  [C]:
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     "Multiply each side by −8, subtract 35 from each side" .
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