Question

Please help!

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 $-5x$

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

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;

$\frac{-2k}{-2}$

This simplifies to;

$k$

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 $2x-7$

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 $x$

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.