The sum of a number and 5 is less then -7

Answer 1

Heya! Philip's answer is good. Still, just in case you want more detail, let me chip in. You should indeed translate "the sum of a number and 5" into math as "x+5", so, as he says,

x+5 < (-7)

Right now you have x+5, but you just want x. So you undo the "+5" by doing the opposite and subtracting 5. That means you have "x" on the left. But the equation only works if you treat both sides fairly: you have to subtract five from both sides.

What is (-7) - 5? It's already negative, but you're just making it more negative. I like to picture the positives and negatives as a giant skyscraper that's also an underground fortress: you're already seven floors underground, and now you're going down five more floors. So it's -12, for a final answer of

x < -12

And maybe you got all that from Philip's answer! This is just how I'd answer a student who's still confused, and sometimes I work with those students too.

Answer 2

Let x be "the number". The sum of the number and 5 is x+5. We want x+5 to be less than -7:

x+5 < -7

x < -12