Classify the following numbers into all applicable sets (Natural $\mathbb{N}$, Whole $\mathbb{W}$, Integer $\mathbb{Z}$, Rational $\mathbb{Q}$, Irrational $\mathbb{I}$, Real $\mathbb{R}$):

1. $7$
2. $-3$
3. $0.25$
4. $\sqrt{5}$

Simplify and classify the following expressions into the most specific number set possible:

1. $\frac{12}{3}$
2. $\sqrt{16}$
3. $\pi + 1$
4. $\frac{0}{5}$

Find the prime factorization of $60$.

Find the GCD of $48$ and $180$.

Find the LCM of $24$, $36$, and $40$.

Evaluate the expression: $15 - 3 \times 2 + 8 \div 4$

Evaluate the expression: $4^2 - 2(5 + 3 \times 2) + 10$

Evaluate the expression: $\frac{3[12 - (4 + 2^2)]}{2^3 - 5}$

Identify the property of real numbers illustrated by each equation:

1. $4 + (x + 3) = (4 + x) + 3$
2. $7 \cdot (2y) = (7 \cdot 2)y$
3. $5(a + 2) = 5a + 10$
4. $x + y = y + x$

Simplify the expression: $-3(2x - 5)$

Simplify the expression completely: $4(3x + 2) - 2(x - 5)$

Simplify the expression: $2x - 3[x - 4(x + 1)]$

State the property of equality that justifies each logical step:

1. If $x = 5$, then $5 = x$.
2. If $a = b$ and $b = 7$, then $a = 7$.
3. $y + 2 = y + 2$
4. If $x = 3$, evaluate $2x + 4$. The step $2(3) + 4$ relies on which property?

Given that $2a + b = c$ and $b = d - a$, prove that $a + d = c$ using properties of equality.

Solve the equation: $|x - 4| = 7$

Solve the equation: $3|2x + 1| - 5 = 10$

Solve the equation: $|3x - 2| + 8 = 4$

Solve the equation: $|x - 2| = 2x - 10$

Solve the inequality and express the answer in interval notation: $4x - 7 > 9$

Solve the inequality and express the answer in interval notation: $-3(x - 2) \ge 15$

Solve the compound inequality: $-8 \lt 2x + 4 \le 10$

Solve the compound inequality: $3x - 1 \le -10$ OR $5x + 2 > 17$