Word Problem: Finding a Number with -5 and 2 in the Equation

[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

Thanks in advance,
Cyril

 

[tiny-tim]

Hi Cyril!

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

 

[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?

 

[tiny-tim]

eugh!

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 ​

 

[HallsofIvy]

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

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

Thanks in advance,
Cyril

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.)