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Calculate and simplify the following expressions involving integers: a) -8 + 6, b) -12 - 20, c) 20 - (-30), d) -9 + (-12), e) 3 - (-8), f) 14 - 28, g) -14 + 26, h) -100 - 200. And simplify: a) 15 + (-

Mathematics

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Here are the solutions to the problems:

1. Calculate the following:

a)

  1. Perform the addition.

    −8+6=−2-8 + 6 = -2

    The result is −2\boxed{-2}.

    b)

  2. Perform the subtraction.

    −12−20=−32-12 - 20 = -32

    The result is −32\boxed{-32}.

    c)

  3. Change the subtraction of a negative number to addition.

    20−(−30)=20+3020 - (-30) = 20 + 30
  4. Perform the addition.

    20+30=5020 + 30 = 50

    The result is 50\boxed{50}.

    d)

  5. Simplify the expression by removing the parentheses.

    −9+(−12)=−9−12-9 + (-12) = -9 - 12
  6. Perform the subtraction.

    −9−12=−21-9 - 12 = -21

    The result is −21\boxed{-21}.

    e)

  7. Change the subtraction of a negative number to addition.

    3−(−8)=3+83 - (-8) = 3 + 8
  8. Perform the addition.

    3+8=113 + 8 = 11

    The result is 11\boxed{11}.

    f)

  9. Perform the subtraction.

    14−28=−1414 - 28 = -14

    The result is −14\boxed{-14}.

    g)

  10. Perform the addition.

    −14+26=12-14 + 26 = 12

    The result is 12\boxed{12}.

    h)

  11. Perform the subtraction.

    −100−200=−300-100 - 200 = -300

    The result is −300\boxed{-300}.

    2. Simplify the following:

    a)

  12. Simplify the expression by removing the parentheses.

    15+(−11)=15−1115 + (-11) = 15 - 11
  13. Perform the subtraction.

    15−11=415 - 11 = 4

    The simplified expression is 4\boxed{4}.

    b)

  14. Perform the subtraction.

    −230−245=−475-230 - 245 = -475

    The simplified expression is −475\boxed{-475}.

    c)

  15. Change the subtraction of a negative number to addition.

    300−(−300)=300+300300 - (-300) = 300 + 300
  16. Perform the addition.

    300+300=600300 + 300 = 600

    The simplified expression is 600\boxed{600}.

    d)

  17. Simplify the expression by removing the parentheses.

    1235+(−1100)=1235−11001235 + (-1100) = 1235 - 1100
  18. Perform the subtraction.

    1235−1100=1351235 - 1100 = 135

    The simplified expression is 135\boxed{135}.

    3. Write down the value of nn that makes each of the following true:

    a)

  19. Calculate the left side of the equation.

    −12+12=n-12 + 12 = n 0=n0 = n

    The value of nn is 0\boxed{0}.

    b)

  20. Isolate nn by adding 10 to both sides of the equation.

    −10+n=6-10 + n = 6 n=6+10n = 6 + 10
  21. Perform the addition.

    n=16n = 16

    The value of nn is 16\boxed{16}.

    c)

  22. Isolate nn by subtracting 10 from both sides of the equation.

    10+n=410 + n = 4 n=4−10n = 4 - 10
  23. Perform the subtraction.

    n=−6n = -6

    The value of nn is −6\boxed{-6}.

    d)

  24. Calculate the left side of the equation.

    −8+2=n−8-8 + 2 = n - 8 −6=n−8-6 = n - 8
  25. Isolate nn by adding 8 to both sides of the equation.

    −6+8=n-6 + 8 = n 2=n2 = n

    The value of nn is 2\boxed{2}.

    e)

  26. Calculate the left side of the equation.

    11−15=−15+n11 - 15 = -15 + n −4=−15+n-4 = -15 + n
  27. Isolate nn by adding 15 to both sides of the equation.

    −4+15=n-4 + 15 = n 11=n11 = n

    The value of nn is 11\boxed{11}.

    f)

  28. Isolate −n-n by adding 7 to both sides of the equation.

    −7−n=−15-7 - n = -15 −n=−15+7-n = -15 + 7 −n=−8-n = -8
  29. Multiply both sides by -1 to find nn.

    n=8n = 8

    The value of nn is 8\boxed{8}.

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