Question

Five times the difference of a number and two is seven more than that number

Answer 1

Answer: The number is: 4 ¼ ; or, write as 4.25 .
_____________________________________________
Explanation:
_______________
We set up the problem as:
_____________________________

5(x − 2) = 7+ x  ;  Solve for "x" (our "unknown number"; which is the answer).
____________________________________________________
Using the "distributive property of multiplication" :
____________________________________________________
a*(b + c) = ab + ac ; AND:

a* (b − c) = ab − ac ; 
_____________________________________________________
Let us take the "left-hand side" of our equation and expand it:
_______________________________________
5(x − 2) = (5*x) − (5*2) = 5x − 10 ;
_________________________________________
and rewrite the equation; substitute our "expanded value" for the "left-hand side";
________________________________
→ 5(x − 2) = 7+ x ;  ↔ 5x − 10 = 7+ x ;
____________________________________
Now, subtract "x" from EACH SIDE of the equation; & add "10" to EACH SIDE of the equation;
________________________________________________
 → 5x − 10 − x + 10 = 7+ x − x + 10 ; 
 _______________________________________________
 → to get:  4x = 17 ;  
________________________________________________
  → Now, divide EACH side of the equation by "4"; to isolate "x" on one side of the equation; and to solve for "x" (our answer);
________________________________________
 → 4x / 4 = 17 / 4; 
__________________________
 → x = 17/4  = 17 ÷ 4 = 4 ¼ ; or, write as 4.25 .
_________________________________________
→ Answer: The number is: 4 ¼ ; or, write as 4.25 .
_____________________________________________
→Let us check our answer: 
_____________________________________________
"Five times the difference of a number and 2"  ;
_____________________________________________
 → 5* (x − 2) = 5 * (4.25 − 2) = 5 * (2.25) = 11.25 ;

→ Is "11.25" ,  SEVEN MORE THAN 4.25??
_________________________________________
  → 11.25  −  4.25 =?? 7 ???  Yes!
__________________________________________