Beginning Algebra

Question

A number increased by the difference between five and the number.

Answer 1

So we have an unknown number, x, and then we add:

x +

What we're adding is the difference of 5 and the number, which means that it also needs to be in parentheses:

(5 - x)

So put together, we have the expression:

x + (5 - x)

This particular expression can be in fact solved. You see, we have a positive x, and we have a negative x, and they in essence cancel each other out as all functions here are additive/subtractive:

Let x = 10

10 + (5 - 10) ⇒ 10 - 5 = 5

Let x = 83:

83 + (5 - 83) ⇒ 83 - 78 = 5

Let x = -21

-21 + (5 + 21) ⇒ -21 + 26 = 5 (we get a +21 in the parentheses because negative*negative=positive)