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anonymous

  • one year ago

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

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  1. mathstudent55
    • one year ago
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    Let the unknown number be x. Using x, how do you write the opposite of a number?

  2. anonymous
    • one year ago
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    a negative number?

  3. mathstudent55
    • one year ago
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    Yes, it's the negative of x, or simply -x

  4. anonymous
    • one year ago
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    6x

  5. mathstudent55
    • one year ago
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    Now we have the opposite of a number is -x. How do you write "six times the opposite of a number"?

  6. mathstudent55
    • one year ago
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    Be careful. 6x is simply "six times a number." We need 6 times the opposite of a number.

  7. anonymous
    • one year ago
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    6x+n?

  8. mathstudent55
    • one year ago
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    The opposite of a number is -x. We need six times -x

  9. mathstudent55
    • one year ago
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    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?

  10. anonymous
    • one year ago
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    yes

  11. mathstudent55
    • one year ago
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    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?

  12. anonymous
    • one year ago
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    ok

  13. mathstudent55
    • one year ago
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    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.

  14. mathstudent55
    • one year ago
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    First, let's simplify 6 * (-x) into simply -6x 237 - 6x = 405 Now we subtract 237 from both sides.

  15. mathstudent55
    • one year ago
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    237 - 6x = 405 -237 -237 ---------------- -6x = 168

  16. mathstudent55
    • one year ago
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    Now we divide both sides by -6 -6x/(-6) = 168/(-6) x = -28

  17. mathstudent55
    • one year ago
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    The number is -28.

  18. anonymous
    • one year ago
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    yup that exactly what i got

  19. mathstudent55
    • one year ago
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    Great.

  20. anonymous
    • one year ago
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    thanks for the help really appreciated that

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spraguer (Moderator)
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