SOLUTION TO QUESTION 1
For [tex]v-6\ge4[/tex]
We add [tex]6[/tex] to both sides of the inequality. This gives us
[tex]v-6+6\ge4+6[/tex]
We simplify to obtain;
[tex]v+0\ge10[/tex]
Hence,
[tex]v\ge 10[/tex]
See the attachment for graph.
SOLUTION TO QUESTION 2
For the inequality [tex]-5x<15[/tex]
We divide both sides by [tex]-5[/tex] and reverse the inequality sign because, we are dividing by a negative number. This implies that;
[tex]\frac{-5x}{-5}> \frac{15}{-5}[/tex]
We simplify to get,
[tex]x>-3[/tex]
See attachment for graph
SOLUTION TO QUESTION 3
For [tex]3k>5k+12[/tex]
We group the terms in [tex]k[/tex] on the left hand side of the inequality,
[tex]3k-5k>12[/tex]
We simplify to obtain;
[tex]-2k>12[/tex]
We divide both sides by [tex]-2[/tex] and reverse the inequality sign because, we are dividing by a negative number again. This implies that;
[tex]\frac{-2k}{-2} <\frac{12}{-2}[/tex]
This simplifies to;
[tex]k<-6}[/tex]
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 [tex]2t\le-4 \: or\:7t\ge 49[/tex]
We divide through the first inequality by 2 and the second inequality by 7 to obtain;
[tex]t\le-2 \: or\: t\ge 7[/tex]
Or
[tex]t\le-2 , t\ge 7[/tex]
SOLUTION TO QUESTION 6
We have [tex]|n+2|=4[/tex]
This implies that;
[tex](n+2)=4[/tex] or [tex]-(n+2)=4[/tex]
This implies that;
[tex]n+2=4[/tex] or [tex]n+2=-4[/tex]
This simplifies to;
[tex]n=4-2[/tex] or [tex]n=-4-2[/tex]
[tex]n=2[/tex] or [tex]n=--6[/tex]
SOLUTION TO QUESTION 7
We have [tex]|2x-7|>1[/tex]
This implies that;
[tex]2x-7>1[/tex] or [tex]-(2x-7)>1[/tex]
We divide the second inequality by negative 1 and reverse the inequality sign.
[tex]2x-7>1[/tex] or [tex]2x-7<-1[/tex]
We group like terms to get,
[tex]2x>1+7[/tex] or [tex]2x<-1+7[/tex]
[tex]2x>8[/tex] or [tex]2x<6[/tex]
We divide both inequalities by 2 to obtain;
[tex]x>4[/tex] or [tex]x<3[/tex]
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.
[tex]A \cup B[/tex]={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.
