Solve the following problems: 1. Inequalities: i) 4(2x+3) < 7−2x ii) 3x+2 > 2x+5. 2. Venn Diagram (Set Theory) with given values.

First, calculate the "only" regions:
$|G \cap K \text{ only}| = |G \cap K| - |G \cap K \cap M| = 14 - 5 = 9$
$|K \cap M \text{ only}| = |K \cap M| - |G \cap K \cap M| = 8 - 5 = 3$
$|G \cap M \text{ only}| = |G \cap M| - |G \cap K \cap M| = 13 - 5 = 8$

Next, calculate the number of people who watched only one channel:
$|G \text{ only}| = |G| - (|G \cap K \text{ only}| + |G \cap M \text{ only}| + |G \cap K \cap M|) = 32 - (9 + 8 + 5) = 32 - 22 = 10$
$|K \text{ only}| = |K| - (|G \cap K \text{ only}| + |K \cap M \text{ only}| + |G \cap K \cap M|) = 24 - (9 + 3 + 5) = 24 - 17 = 7$
$|M \text{ only}| = |M| - (|K \cap M \text{ only}| + |G \cap M \text{ only}| + |G \cap K \cap M|) = 22 - (3 + 8 + 5) = 22 - 16 = 6$

The Venn diagram would show three overlapping circles for G, K, and M.

• The center intersection (G $\cap$ K $\cap$ M) would be 5.
• The intersection of G and K only would be 9.
• The intersection of K and M only would be 3.
• The intersection of G and M only would be 8.
• The G only region would be 10.
• The K only region would be 7.
• The M only region would be 6.

Find the number of people who

From the calculations above, the number of people who watched MTV only is $\boxed{6}$.

3. Ratio and Proportion

Lois and Gina share $100.00 in the ratio 2:5.