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}

SOLUTION TO QUESTION 1

For

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

We simplify to obtain;

Hence,

See the attachment for graph.

SOLUTION TO QUESTION 2

For the inequality

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

We simplify to get,

See attachment for graph

SOLUTION TO QUESTION 3

For

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

We simplify to obtain;

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

This simplifies to;

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

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

Or

SOLUTION TO QUESTION 6

We have

This implies that;

or  

This implies that;

or  

This simplifies to;

or  

or  

SOLUTION TO QUESTION 7

We have

This implies that;

or

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

or

We group like terms to get,

or

or

We divide both inequalities by 2 to obtain;

or

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.

={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.