1. **Understanding Linear Inequalities:** Linear inequalities are like equations but instead of an equals sign, they use inequality signs such as $<$, $>$, $\leq$, or $\geq$. The goal is to find all values of the variable that make the inequality true. **Key rules:** - You can add or subtract the same number on both sides without changing the inequality. - You can multiply or divide both sides by a positive number without changing the inequality. - If you multiply or divide both sides by a negative number, you must reverse the inequality sign. 2. **Representing inequalities on a number line:** - Use an open circle for $<$ or $>$ (not including the number). - Use a closed circle for $\leq$ or $\geq$ (including the number). - Shade the line to the left for $<$ or $\leq$. - Shade the line to the right for $>$ or $\geq$. 3. **Solving example inequalities from your list:** **Part 2a: $3 < b < 33$** - This means $b$ is greater than 3 and less than 33. - The integers satisfying this are all whole numbers between 4 and 32. - So, $b = 4, 5, 6, ..., 32$. **Part 2b: $7 < h \leq 19$** - $h$ is greater than 7 and less than or equal to 19. - Integers are $8, 9, 10, ..., 19$. **Part 2c: $18 \leq e \leq 27$** - $e$ is between 18 and 27, including both. - Integers: $18, 19, ..., 27$. **Part 2d: $-3 \leq f < 0$** - $f$ is greater than or equal to -3 and less than 0. - Integers: $-3, -2, -1$. **Part 2e: $-3 \leq f \leq 0$** - $f$ is between -3 and 0, including both. - Integers: $-3, -2, -1, 0$. **Part 2f: $2.5 < m < 11.3$** - $m$ is greater than 2.5 and less than 11.3. - Integers: $3, 4, 5, ..., 11$. **Part 2g: $-7 < g \leq -4$** - $g$ is greater than -7 and less than or equal to -4. - Integers: $-6, -5, -4$. **Part 2h: $\pi < r < 2\pi$** - Approximate $\pi \approx 3.14$, $2\pi \approx 6.28$. - Integers between 3.14 and 6.28 are $4, 5, 6$. **Part 2i: $\sqrt{5} < w < \sqrt{18}$** - Approximate $\sqrt{5} \approx 2.24$, $\sqrt{18} \approx 4.24$. - Integers: $3, 4$. **Summary:** - To solve inequalities, understand the inequality signs and represent the solution on a number line. - For integer solutions, find all whole numbers within the interval.