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cluponka [151]
3 years ago
5

Please help!

Mathematics
1 answer:
Ivenika [448]3 years ago
3 0

<u>SOLUTION TO QUESTION 1</u>

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.


<u>SOLUTION TO QUESTION 2</u>


For the inequality -5x


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


\frac{-5x}{-5}> \frac{15}{-5}


We simplify to get,

x>-3


See attachment for graph


<u>SOLUTION TO QUESTION 3</u>


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;


\frac{-2k}{-2}


This simplifies to;


k

See attachment for graph.


<u>SOLUTION TO QUESTION 4</u>

Given the set {5,10,15}

All the possible subsets are;

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



<u>SOLUTION TO QUESTION 5</u>

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



<u>SOLUTION TO QUESTION 6</u>

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


<u>SOLUTION TO QUESTION 7</u>

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

We group like terms to get,


2x>1+7 or 2x


2x>8 or 2x

We divide both inequalities by 2 to obtain;


x>4 or x


<u>SOLUTION TO QUESTION 8</u>

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}


<u>SOLUTION TO QUESTION 9</u>

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.



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