anonymous
  • anonymous
The sum of 237 and six times the opposite of a number is 405. What is the number? A) -28 B) -24 C) 30 D) 32
Mathematics
katieb
  • katieb
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mathstudent55
  • mathstudent55
Let the unknown number be x. Using x, how do you write the opposite of a number?
anonymous
  • anonymous
a negative number?
mathstudent55
  • mathstudent55
Yes, it's the negative of x, or simply -x

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anonymous
  • anonymous
6x
mathstudent55
  • mathstudent55
Now we have the opposite of a number is -x. How do you write "six times the opposite of a number"?
mathstudent55
  • mathstudent55
Be careful. 6x is simply "six times a number." We need 6 times the opposite of a number.
anonymous
  • anonymous
6x+n?
mathstudent55
  • mathstudent55
The opposite of a number is -x. We need six times -x
mathstudent55
  • mathstudent55
We are not adding anything yet. six times a number is 6x the opposite of a number is -x six times the opposite of a number is 6 * (-x) ok so far?
anonymous
  • anonymous
yes
mathstudent55
  • mathstudent55
OK. Now we deal with 237. The "sum" means an addition. The sum of 237 and six times the opposite of a number is 237 + 6 * (-x) Ok?
anonymous
  • anonymous
ok
mathstudent55
  • mathstudent55
Now we finally take care of the 405. 237 + 6 * (-x) = 405 Now we have an equation. We can solve the equation and find the number.
mathstudent55
  • mathstudent55
First, let's simplify 6 * (-x) into simply -6x 237 - 6x = 405 Now we subtract 237 from both sides.
mathstudent55
  • mathstudent55
237 - 6x = 405 -237 -237 ---------------- -6x = 168
mathstudent55
  • mathstudent55
Now we divide both sides by -6 -6x/(-6) = 168/(-6) x = -28
mathstudent55
  • mathstudent55
The number is -28.
anonymous
  • anonymous
yup that exactly what i got
mathstudent55
  • mathstudent55
Great.
anonymous
  • anonymous
thanks for the help really appreciated that

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