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what is the value of x in the following equation: 3x-15=4x+36
a.21
b.-51
c.-21
d. none of these

[B]:  - 51 .

Explanation:

Given: 3x − 15 = 4x + 36 ;  Solve for "x" .

Let us subtract: "3x" from EACH side of the equation; AND
           add: "15 to EACH side of the equation: 

 → 3x − 15 − 3x + 15 = 4x + 36 − 3x + 15 ; 

 to get:

 → 0 = x + 51 ;

 →  Subtract "51" from EACH side of the equation; to isolate "x" on one side of the equation; and to solve for "x" ;

 → 0 − 51 = x + 51 − 51 ;

 →    - 51 = x ; ↔ x = - 51 ; which is: "Answer choice: [B]: -51".

→ Now, let us check our answer, "x = -51 ; by plugging in "-51" for "x" in the original equation, and seeing in both sides of the equation hold true when x =  - 51 ;

→ Given:  3x − 15 = 4x + 36 ;  
 
    →  Substitute "- 51 for "x" ;

→  Start with the "left-hand side" of the equation: 

→ 3x − 15 = (3*-51) − 15 = -153 − 15 = -168 ; when x = -51 ;

→ Then, let us examine the "right-hand side" of the equation: 

→ 4x + 36 ;  Substitute "-51" for "x" ; 

    →  (4*-51) + 36 = -204 + 36 = -168

→ Does the "left hand side" of equation = the "right-hand side of the equation" when: x = -51???

 → That is, when x = -51, does: - 168 =? -168 ?? Yes!