Let's go through the practice quiz step-by-step and cover the material you'll need for tomorrow's quiz.

1. Solving Absolute Value Equations

Problem: Solve for $n$:
$3 − 7 + 2|−4 − 𝑛| = − 9$

Solution Approach:

1. Simplify the equation by isolating the absolute value term.
2. Remove the absolute value by considering both positive and negative cases.
3. Solve for $n$ in both cases.

2. Finding Distance Using Absolute Value

Problems:

1. Express the distance between $-22$ and $-5$ using absolute value.
2. Express the distance between $-18$ and $7$ using absolute value.

Solution Approach:

1. The distance between two points $a$ and $b$ is given by $|a - b|$.
2. Calculate $|-22 - (-5)|$ and $|-18 - 7|$.

3. Simplifying Algebraic Expressions

Problem 1: $-\frac{1}{3}(9𝑦 − 3) + [(-8𝑦) + (8𝑦)]$

Problem 2: $28 ÷ 4 \cdot 6 + \frac{32+42}{11 + 5 - 22}$

Solution Approach:

1. Distribute and combine like terms in Problem 1.
2. Use the order of operations (PEMDAS) in Problem 2.

4. Comparing Expressions with Inequalities

Problem: Fill in the blank with $>, <,$ or $=$ for expressions like: $\frac{60}{90 - 6} \quad \text{and} \quad \frac{13}{17} \cdot 17$

Solution Approach:

1. Simplify each side of the inequality.
2. Compare the simplified values.

5. Translating Words to Algebraic Expressions

Problem: "The difference between the product of seven and a number and negative 4 times the number."

Solution Approach:

1. Let the unknown number be $x$.
2. Write the product of 7 and $x$, then subtract the product of $-4$ and $x$.

6. Simplifying Expressions with Exponents

Problems:

1. $(𝑥^{−3}𝑦^{−2})^4 \cdot (𝑥^3)^3 \cdot 2𝑥^{−2}$
2. $\frac{(𝑥^{−3})^4𝑥^4}{2𝑥^{−3}}$

Solution Approach:

1. Apply the power rule $(a^m)^n = a^{mn}$.
2. Use the product and quotient rules for exponents.

7. Rationalizing and Simplifying Complex Fractions

Problem: Simplify expressions like: $\frac{(2𝑥^0𝑦^2)^{−3} \cdot 2𝑥^3𝑦}{(𝑥^3𝑦^4𝑧^2) \cdot (𝑥^{−4}𝑧^3)}$

Solution Approach:

1. Simplify the terms separately.
2. Combine like terms and apply the rules for exponents.

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If you have any specific questions on these, or if you want a more detailed explanation, let me know!

Relative Questions to Expand:

1. What are the steps for solving absolute value inequalities?
2. How do you determine the distance between two points on a coordinate plane?
3. How do you simplify expressions with multiple variables and exponents?
4. What are the rules for comparing rational expressions?
5. How can word problems be translated into algebraic expressions?

Tip: For simplifying complex expressions, always break them down into smaller parts and use the properties of exponents systematically.