Which represents the solution set of 5(x+5)< 85? a.) x< 12 b.) x> 12 c.) x< 16 d.) x> 16

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 " .