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

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 .

→ The number is: 4 ¼ ; or, write as 4.25 .

→Let us check our  

"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!

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