Question

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

Answer 1

The correct answer choice is:
______________________________________________
[C]: "Multiply each side by −8, subtract 35 from each side" .
_______________________________________________
Step-by-step explanation:
_______________________________________________
Given: "
`(-1)/(8)` (x + 35) = -7 " ;

We can START by multiply each side of the equation by "-8" to completely get rid of the "
`(-1)/(8)`" fraction on the "left-hand-side" of the equation:

since: "
`(-1)/(8)` * -8 = 1 ; and: "1" , multiplied by any given value, is equal to that given value; so in effect, the "1" becomes eliminated.

"
`(-1)/(8)` * -8 =


`(-1)/(8)` *
`(-8)/(1)` =



`((-1*-8))/((8* 1))` =
`(8)/(8)` = 1 .
____________________________________________________
So, given: "
`(-1)/(8)` (x + 35) = -7 " ; ;

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

→ -8 * {
`(-1)/(8)` (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" .
______________________________________________________