Solve the following equation: -7x = 42solve the following equation: 2(x - 4) - 15 = -27solve the following equation: 6x - 2 = 4(x + 1)

Answers:

   1)    " x = -6 "  .

   2)  " x = 8 " .

   3)   " x = 3 " .


 
Explanation:

  1)   "  -7x  =  42 " ;  Solve for "x" ;  

Divide each side by "-7" ; 

-7x / -7 = 42/ -7 ; 

  x = - 6 .


2)   " 2(x − 4) − 15  =  - 7 " ;  Solve for "x" ; 

     Add "15" to each side of the equation ; 

      " 2(x − 4) − 15 + 15  =  - 7  + 15 ; 

  → " 2(x − 4) = 8 "  ;

Now, divide each side of the equation by "2" ; 

      →    [ 2(x − 4) ] / 2  =  8 / 2 ;

 to get:  "(x − 4) = 4 " ; 

Add "4" to each side of the equation; 
 to isolate "x" on one side of the equation; and to solve for "x" ; 

     →  x − 4 + 4 = 4 + 4 ;

to get:    " x = 8 " .


3)  "6x  − 2  = 4(x  +  1 ) "

   →  Factor out a "2" from "6x  − 2" :

   →  " 2(3x  −  1) " ;

Rewrite the equation as:

   →  " 2(3x  −  1)  = 4(x  +  1) '" ; 

Now, divide EACH SIDE of the equation by "2" ; 

   →  " [ 2(3x  −  1) ] / 2  =  [ 4(x + 1) ] / 2 " ;

to get:

   →  3x − 1  = 2(x + 1) .

Now, let us simplify the "right-hand side" of the equation ; 

Note the "distributive property of multiplication" :

a (b + c)  = ab + ac ;

  As such:  " 2(x + 1) =  (2*x) + (2*1`) = 2x + 2 ; 

Now, rewrite the equation:

   →  " 3x − 1   =  2x + 2 " ;

Subtract "2x" from each side of the equation; & Add "1" to each side of the equation:
 
  →  " 3x  − 1  − 2x + 1  =  2x + 2  −  2x + 1 ; 

to get: 

x  = 3 .