# Help with a word problem

1. Jun 28, 2011

### Cyrilshark

The word problem: If the product of a number and -5 is reduced by 2, the result is 26 less than twice the opposite of the number. What is the number?

I wrote it out like this:
n x (-5) - 2 = 2(-n) - 26

I'm really at a loss here. Normally when there's a variable, my teacher says to get the variable alone, but when there's two that share a number, I don't know what to do besides pick random numbers and see what happens :P

Cyril

2. Jun 28, 2011

### tiny-tim

Hi Cyril!

Just shove all the n's over to the LHS, and everything else to the RHS.

3. Jun 28, 2011

### Cyrilshark

Haha thanks :D

So add 7 to the left to get rid of the -5 and - 2 (and add it to the right of course), but how do you move the variable from the right?

4. Jun 28, 2011

### tiny-tim

eugh! :yuck:

perhaps i'd better start you off

n x (-5) - 2 = 2(-n) - 26​

let's rewrite that as

-5n - 2 = -2n - 26 …​

carry on from there

5. Jun 28, 2011

### HallsofIvy

It would be better to write this as -5n- 2= -2n- 26

So combine the two: add 2n to both sides, add 2 to both sides

(If you don't like negatives, you could start by multiplying both sides by -1 to get
5n+ 2= 2n+ 26. Now subtract 2n from both sides, subtract from both sides.)