Question

Please help!

1. Solve The Inequality & Graph The Solution: v-6≥4

2. Solve The Inequality & Graph The Solution: -5x<15

3. Solve The Inequality & Graph The Solution: 3k>5k+12

4. List The Subsets Of The Set: {5, 10, 15}

5. Solve The Compound Inequality: 2t≤-4 or 7t≥49

6. Solve The Equation. If There Is No Solution, Write No Solution (Show Work): |n+2|=4

7. Solve The Equation. If There Is No Solution, Write No Solution (Show Work): |2x-7|>1

8. Given A={1,2,3,4,5,6,7,8,9} & B={2,4,6,8}, What Is AuB ( The u is that one weird u like symbol)

9. Draw A Venn Diagram To Represent The Intersection & Union Of The Sets: P={1,5,7,9,13}, R={1,2,3,4,5,6,7}, & Q={1,3,5}

Answer 1

SOLUTION TO QUESTION 1

For
`v-6\ge4`

We add
`6` to both sides of the inequality. This gives us

`v-6+6\ge4+6`

We simplify to obtain;

`v+0\ge10`

Hence,

`v\ge 10`

See the attachment for graph.

SOLUTION TO QUESTION 2

For the inequality
`-5x<15`

We divide both sides by
`-5` and reverse the inequality sign because, we are dividing by a negative number. This implies that;

`(-5x)/(-5)> (15)/(-5)`

We simplify to get,

`x>-3`

See attachment for graph

SOLUTION TO QUESTION 3

For
`3k>5k+12`

We group the terms in
`k` on the left hand side of the inequality,

`3k-5k>12`

We simplify to obtain;

`-2k>12`

We divide both sides by
`-2` and reverse the inequality sign because, we are dividing by a negative number again. This implies that;

`(-2k)/(-2) <(12)/(-2)`

This simplifies to;

`k<-6}`

See attachment for graph.

SOLUTION TO QUESTION 4

Given the set {5,10,15}

All the possible subsets are;

{}, {5}, {10}, {15}, {5,10}, {5,15}, {10,15}, and {5,10,15}

SOLUTION TO QUESTION 5

For
`2t\le-4 \: or\:7t\ge 49`

We divide through the first inequality by 2 and the second inequality by 7 to obtain;

`t\le-2 \: or\: t\ge 7`

Or

`t\le-2 , t\ge 7`

SOLUTION TO QUESTION 6

We have
`|n+2|=4`

This implies that;

`(n+2)=4` or
`-(n+2)=4`

This implies that;

`n+2=4` or
`n+2=-4`

This simplifies to;

`n=4-2` or
`n=-4-2`

`n=2` or
`n=--6`

SOLUTION TO QUESTION 7

We have
`|2x-7|>1`

This implies that;

`2x-7>1` or
`-(2x-7)>1`

We divide the second inequality by negative 1 and reverse the inequality sign.

`2x-7>1` or
`2x-7<-1`

We group like terms to get,

`2x>1+7` or
`2x<-1+7`

`2x>8` or
`2x<6`

We divide both inequalities by 2 to obtain;

`x>4` or
`x<3`

SOLUTION TO QUESTION 8

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

and

B={2.4,6,8}

The union of A and B, are the elements in set A or set B or both.

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

SOLUTION TO QUESTION 9

Given:

P={1,5,7,9,13}

R={1,2,3,4,5,6,7}

and

Q={1,3,5}

We apply our understanding of subsets to draw the Venn diagram.

See attachment for the Venn Diagram.