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 " .
_________________________________________________
