Solve the following set of inequality: 2x + 4 >= 18

1. a) Biology is the scientific study of life. It explores the structure, function, growth, evolution, distribution, and classification of all living organisms.

b) Mathematics is applied in various fields, including:
i. Engineering
ii. Physics
iii. Computer Science
iv. Economics
v. Medicine

2. a) i. Algebra: The study of mathematical symbols and the rules for manipulating these symbols. It involves solving equations and understanding relationships between quantities.
   • Examples: Solving $2x + 5 = 11$ for $x$. Using variables like $a^2 - b^2 = (a-b)(a+b)$. ii. Geometry: The study of shapes, sizes, positions, and properties of space. It deals with points, lines, angles, surfaces, and solids.
   • Examples: Calculating the area of a triangle. Determining the volume of a cylinder. iii. Statistics: The science of collecting, analyzing, interpreting, presenting, and organizing data. It helps in making informed decisions based on numerical information.
   • Examples: Calculating the average score of a class. Predicting election outcomes based on survey data.

b) Yes, learning mathematics is important in our daily life for the following reasons:
i. It develops critical thinking and problem-solving skills.
ii. It is essential for managing personal finances and budgeting.
iii. It helps in understanding and interpreting data from news and reports.
iv. It is fundamental for technological literacy and understanding how modern devices work.

3. a) i. To represent $x \ge 2\frac{3}{5}$ on a number line: Convert $2\frac{3}{5}$ to a decimal: $2 + \frac{3}{5} = 2 + 0.6 = 2.6$. The inequality is $x \ge 2.6$. On a number line, draw a closed circle at 2.6 and shade the line to the right.

\begin{tikzpicture} \draw[<->] (-0.5,0) -- (5.5,0); \foreach \x in {0,1,2,3,4,5} \draw (\x,0.1) -- (\x,-0.1) node[below] {\x}; \filldraw[black] (2.6,0) circle (2pt); \draw[line width=1.5pt, ->] (2.6,0) -- (5.5,0); \end{tikzpicture}

ii. To represent $\frac{5}{2} \le x < 4$ on a number line:
Convert $\frac{5}{2}$ to a decimal: $\frac{5}{2} = 2.5$.
The inequality is $2.5 \le x < 4$.
On a number line, draw a closed circle at 2.5 and an open circle at 4. Shade the line segment between these two points.

\begin{tikzpicture} \draw[<->] (-0.5,0) -- (5.5,0); \foreach \x in {0,1,2,3,4,5} \draw (\x,0.1) -- (\x,-0.1) node[below] {\x}; \filldraw[black] (2.5,0) circle (2pt); \draw[white, line width=3pt] (4,0) circle (2pt); % To make it look like an open circle \draw[black] (4,0) circle (2pt); \draw[line width=1.5pt] (2.5,0) -- (4,0); \end{tikzpicture}

b) Five rational numbers equivalent to $\frac{3}{2}$ are:
i. $\frac{3 \times 2}{2 \times 2} = \frac{6}{4}$
ii. $\frac{3 \times 3}{2 \times 3} = \frac{9}{6}$
iii. $\frac{3 \times 4}{2 \times 4} = \frac{12}{8}$
iv. $\frac{3 \times 5}{2 \times 5} = \frac{15}{10}$
v. $\frac{3 \times 10}{2 \times 10} = \frac{30}{20}$

4. a) Calculate Mr. Greyson's monthly savings. Total Salary = Tsh 450,000 Amount spent on food (first part) = $\frac{1}{5} \times 450,000 = 90,000$ Tsh Remaining salary = $450,000 - 90,000 = 360,000$ Tsh Amount spent on food (second part) = $\frac{1}{2} \times 360,000 = 180,000$ Tsh Remaining salary after second food expense = $360,000 - 180,000 = 180,000$ Tsh Amount spent on miscellaneous = $\frac{1}{2} \times 180,000 = 90,000$ Tsh Remaining salary after miscellaneous = $180,000 - 90,000 = 90,000$ Tsh His monthly savings = 90,000 Tsh. His monthly savings is $\boxed{\text{Tsh 90,000}}$.

b) The answer in part (a) is Tsh 90,000. This is a rational number because it can be expressed as a fraction of two integers, for example, $\frac{90000}{1}$.

5. a) i. 23.126666... in recurring notation is $\boxed{23.12\dot{6}}$. ii. 12.6231 in long form (expanded form) is $\boxed{1 \times 10^1 + 2 \times 10^0 + 6 \times 10^{-1} + 2 \times 10^{-2} + 3 \times 10^{-3} + 1 \times 10^{-4}}$.

b) The numbers such as $\pi, e, e + \pi, 2\pi$ and other similar numbers are called irrational numbers.

6. a) Solve the inequality $2x + 4 \ge 18$.