Question

Which represents the solution set of 5(x+5)<85?

Answer 1

Isolate the VARIABLE by dividing each side by FACTROS that don't contain the VARIABLE .
YOUR answer is x<12

Answer 2

The correct answer is:  [A]:  " x < 12 " .
__________________________________________________
Given:
__________________________________________________
  " 5(x + 5) < 85 " ;  Simplify/ solve for "x" ; 
__________________________________________________
Method 1)
__________________________________________________

Note the "distributive property of multiplication" :
__________________________________________________
  a(b +  c)  =   ab + ac ;

  a(b – c)   =  ab – ac .
__________________________________________________
So, take the "left-hand side" of the inequality; and expand:
__________________________________________________
  →  5(x + 5) = (5*x) + (5*5) = 5x + 25 ; 

Now, rewrite the inequality:

  →  5x + 25 < 85  ;

Subtract "25" from each side of the inequality ; 

  →  5x + 25 – 25 < 85 – 25  ;

to get:
_______________________________________
  →  5x  <  60  ;

Divide each side of the inequality by "5" ; 

  →  5x / 5  <  60 / 5 ; 

  →  x  <  12 ;  which is:  Answer choice:  [A]:  " x < 12 " .
_______________________________________

Method 2)
_______________________________________
Given:
_______________________________________
 " 5(x + 5) < 85 " ;  Simplify/ solve for "x" ; 
_______________________________________
 Divide EACH SIDE of the equation by "5" ; 

  [5(x + 5) ] / 5 < 85 / 5 ; 

to get: 

  →  x + 5 < 17 ; 

Subtract "5" from EACH SIDE of the inequality:

  →  x + 5 – 5  <  17 – 5 ; 

to get:

  →  x  <  12  ;  which is:  Answer choice:  [A]:  " x < 12 " .
_________________________________________________