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 side

Multiply each side by negative one over eight , subtract 35 from each side

Multiply each side by −8, subtract 35 from each side

Multiply each side by −8, add 35 to each side

Question

05-12-2017
Mathematics

contestada

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 side

Multiply each side by negative one over eight , subtract 35 from each side

Multiply each side by −8, subtract 35 from each side

Multiply each side by −8, add 35 to each side

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JonHenderson55 JonHenderson55 · Answer 1 · 2017-12-05T18:16:33+01:00

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