How do you simplify algebraic expressions with absolute values, parentheses, and negative numbers?

Use the order of operations: simplify inside parentheses and absolute values first, then multiply or divide, and finally add or subtract.

How do you solve a multi-step equation such as 5(x - 2) = 3x + 4?

Distribute first, combine like terms, then isolate the variable using inverse operations. For this equation, x = 7.

How are compound and absolute value inequalities solved in Algebra 2?

Solve each inequality carefully, reverse the inequality when multiplying or dividing by a negative, and express the result as an interval or combined solution set.

Free online course Algebra 2 Course

Duration of the online course: 3 hours and 3 minutes

New

Build confidence in Algebra 2 fast with a free online course: simplify expressions, solve equations and inequalities, and practice with guided problems.

In this free course, learn about

Simplify algebraic expressions with sums/differences, including negatives and parentheses
Use absolute value in simplifying numerical expressions (e.g., 8 - |...| - 12 - (-9))
Apply distributive property and combine like terms in linear expressions (e.g., 1/2(2a-4b+6))
Simplify products with integers, fractions, and signs; use order of operations
Evaluate expressions with exponents, including negative bases (e.g., (-1)^3, (-2)^4)
Simplify algebraic expressions with multiplication across parentheses (e.g., t(2w-9)-2(2t+7))
Simplify division expressions, including complex fractions and exponent rules
Evaluate rational expressions at given values while noting domain restrictions
Solve multi-step linear equations with distribution and variables on both sides
Rearrange linear equations to solve for one variable in terms of another (literal equations)
Solve one-variable linear inequalities and interpret solution sets
Solve compound inequalities (AND/OR) and write solutions in interval notation
Solve absolute value inequalities and express solutions as intervals or unions

About the free online course

Strengthen your Algebra 2 skills with a focused, practice-driven free online course built to help you think clearly and work accurately through increasingly challenging problems. If you have ever felt stuck when expressions get messy or when equations take more than one step to solve, this course helps you rebuild your foundation and turn common rules into reliable habits you can use on tests and homework.

You start by simplifying algebraic expressions involving sums and differences, learning to handle signs, grouping, and absolute value without second-guessing yourself. From there, you move into multiplication and distribution so you can simplify products, work with powers, and combine like terms efficiently. Step by step, you learn how to spot structure in an expression and choose the simplest path to a clean result.

As you progress, division and rational expressions become more manageable. You practice simplifying numerical and algebraic fractions, evaluating expressions at specific values, and understanding why certain values are not allowed. These skills are essential for avoiding common mistakes and for preparing for more advanced algebra topics.

The course also guides you through multi-step equations, showing how to isolate variables confidently and check your work. You then expand into inequalities, including compound and absolute value inequalities, learning how solution sets work and how to interpret them correctly. With paired exercises, you get repeated opportunities to apply each method until it feels natural.

Whether you are catching up, reinforcing what you learned in class, or preparing for exams, this course gives you a structured way to practice core Algebra 2 problem-solving and build lasting confidence.

Course content

Video class: 01 - Simplifying Algebraic Expressions that Involve Sums and Differences, Part 1 19m
Exercise: Simplify the expression 8 - | -3 + 5 | - 12 - (-9)
Video class: 02 - Simplifying Expressions That Involve Sums And Differences, Part 2 04m
Exercise: Simplify the expression: 1/2(2a - 4b + 6)
Video class: 03 - Simplifying Expressions in Algebra that Involve Multiplication, Part 1 17m
Exercise: Simplify 9 * (-1/7) * (1/3) * (-28)
Video class: 04 - Simplifying Expressions That Involve Multiplication, Part 2 04m
Exercise: Simplify the expression (-1)^3 times (-2 - 2) times (-6) times (-4)
Video class: 05 - Simplifying Expressions That Involve Multiplication, Part 3 03m
Exercise: Simplify t(2w - 9) - 2(2t + 7)
Video class: 06 - Simplifying Algebraic Expressions that Involve Division, Part 1 15m
Exercise: Simplify the expression: [(-16 × 3 ÷ 2)] ÷ [(-2)^4]
Video class: 07- Simplifying Expressions That Involve Division, Part 2 04m
Exercise: Simplify the expression: (3^2 - 5^2) / (3 + -5)
Video class: 08 - Simplifying Expressions That Involve Division, Part 3 03m
Exercise: Evaluate y(y − 3)/(y − 2) at y = 1

Video class: 09 - Solving Multi-Step Equations in Algebra, Part 1 (Two Step Equations 16m
Exercise: Solve for x in 5(x - 2) = 3x + 4
Video class: 10 - Solving Multi-Step Equations, Part 2 04m
Video class: 11 - Solving Multi step Equations, Part 3 03m
Exercise: Solve for x in terms of y: 2x - 5y = 10

Video class: 12 - Solving 20m
Exercise: Which value satisfies the inequality -5x < 10?
Video class: 13 - Solving Inequalities With One Variable, Part 2 04m
Exercise: Solve the inequality: 5(2x + 3) >= 2(x - 3) + x. Which set describes all solutions?
Video class: 14 - Solving 21m
Exercise: Solve the compound inequality 0 ≤ x − 2 < 3
Video class: 15 - Solving Compound Inequalities, Part 2 05m
Exercise: Solve the compound inequality: -1 > 2x - 5 > -9. Which solution set is correct
Video class: 16 - Solving Compound Inequalities, Part 3 05m
Exercise: Solve the compound inequality: 7x - 1 > x + 11 OR -11x > -33. What is the solution set?

Video class: 17 - Solving 23m
Exercise: Solve the inequality |3 - 2x| < 5
Video class: 18 - Solving Absolute Value Inequalities, Part 2 05m
Video class: 19 - Solving Absolute Value Inequalities, Part 3 04m
Exercise: Solve the inequality and choose the correct solution set: |2x - 1| + 3 ≤ 6

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