Question

PLEASE HELP! WILL MARK BRAINLIEST

Answer 1

1)

v - 6 ≥ 4

  +6   +6

v      ≥ 10

Graph: 10 -----------------→  the dot at 10 is filled in because of the "equal to" symbol

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2)

-5x < 15

$\frac{-5x}{-5} > \frac{15}{-5}$  divided by a negative so the symbol flipped

x > -3

Graph: -3 o------------------→ the dot at -3 is NOT filled in because it's NOT "equal to"

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3)

3k > 5k + 12

-5k  -5k      

-2k >          12

$\frac{-2k}{-2} < \frac{12}{-2}$   divided by a negative so the symbol flipped

k < -6

Graph: ←------------o -6   the dot at -6 is NOT filled in because it's NOT "equal to"

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5)

2t ≤ 4      or    7t ≥ 49

$\frac{2t}{2} \leq\frac{4}{2}$      or    $\frac{7t}{7} \geq \frac{49}{7}$

 t ≤ 2      or      t ≥ 7

Graph: ←------- 2        7 ---------→   the dots at 2 and 7 are filled in

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6)

| n + 2 | = 4

n + 2 = 4      or     n + 2 = -4

    -2   -2                 -2   -2

n      = 2        or     n       = -6

Answer: n = {2, -6}

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7)

| 2x - 7 | > 1

2x - 7 > 1       or     2x - 7 < -1

     +7  +7                 +7   +7

2x      > 8       or     2x     <  6

    $\frac{2x}{2} > \frac{8}{2}$             or       $\frac{2x}{2} < \frac{6}{2}$

    x > 4          or         x < 3

Graph: ←----------o 3      4 o------------→

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8)

A = {1, 2, 3, 4, 5, 6, 7, 8, 9}    B = {2, 4, 6, 8}

A U B = {1, 2, 3, 4, 5, 6, 7, 8, 9}    union combines both sets

A ∩ B =  {2, 4, 6, 8}   intersection includes only those that are in BOTH sets

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9)

P = {1, 5, 7, 9, 13}   R = { 1, 2, 3, 4, 5, 6, 7}    Q = {1, 3, 5}

P ∩ R ∩ Q = {1, 5}

P ∩ R = {7}  disregard 1 & 5 since they are already in P∩Q∩R

R ∩ Q = {3}  disregard 1 & 5 since they are already in P∩Q∩R

P ∩ Q = { }  disregard 1 & 5 since they are already in P∩Q∩R

P no intersection = {9, 13)

R no intersection = {2, 4, 6}

Q no intersection = {  }

If you can't figure out how to draw it based on the information I provided, please see the attached diagram. Note: Usially, you would only identify P, Q, R.  I identified the intersections so you would understand why those specific numbers are placed in the designated sections.