the difference of 73 and a number x is 17

Question

this is algebra one 

Answer 1

Consider it with a smaller difference first.  If the difference between 73 and x were 1, what would x have to be?

 

Clearly, it would have to be 72 - one less than 73, in order to have a difference of 1.  Similarly, if the difference of 73 and x were 3, then x would have to be 70, three less than 73.

 

Here, the difference between 73 and x is 17.  So x must be 17 less than 73.  73 - 17 = 56.

 

Algebraically, we set this situation up with an equation.

73 - x = 17.

 

On the left hand side, you have "the difference of 73 and x," "is" as an equals sign, and then 17 on the right hand side.

You solve it by adding x to both sides of the equation

 

73 - x + x = 17 + x

 

Canceling out the x's on the left

73 = 17 + x

 

Subtracting 17 from both sides, which likewise cancels out the 17 on the right

73 - 17 = x

 

And simplifying.

56 = x

Answer 2

Difference is the result of subtraction. "Is" is usually the same as "=."

 

73 - x = 17          subtract 73 from both sides

-x = -56               multiply both sides by -1

x = 56