GED® Algebra: Advanced Inequalities & Applications
A harder follow-up to GED® Algebra: Inequalities Mastery. Students solve advanced linear inequalities, compound inequalities, absolute-value inequalities, quadratic and rational inequalities, systems of inequalities, and difficult GED®-style applications. The course emphasizes interval notation, endpoint logic, sign charts, testing regions, and step-by-step reasoning.
📚 Course Curriculum
Advanced inequalities are not about memorizing more symbols. They are about tracking regions of possible answers. An equation usually asks, "Which value makes this exactly …
Open trial session →Interval notation is a compact way to write solution sets. Symbols:. Parentheses \(( \ )\): endpoint is not included. Brackets \([ \ ]\): endpoint is …
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Harder linear inequalities often include parentheses on both sides, negative coefficients, or variables on both sides. Example 1:. Distribute and combine:. Add 7 and divide:. …
Open trial session →Compound inequalities combine two conditions. AND means overlap:. The value must satisfy both sides. OR means union:. Either region works. Example 1:. Subtract 6 from …
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Absolute value means distance. This gives two major patterns. Less than means inside:. Example 1:. Inside pattern:. Add 4:. Example 2:. Outside pattern:. Solve:. Example …
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A quadratic inequality has an \(x^2\) term. The solution is found by looking where the parabola is above or below the x-axis. [[figure:parabola A quadratic …
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A sign chart tracks whether each factor is positive or negative in each interval. Example:. Critical points:. They split the number line:. \((-\infty,-2)\). \((-2,1)\). \((1,4)\). …
Open trial session →A rational inequality has a variable in a denominator. Denominators create excluded values. Example 1:. Critical values:. Numerator zero: \(x=3\). Denominator zero: \(x=-2\), excluded. Test …
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A system of inequalities asks for points that satisfy all inequalities at the same time. The solution is the overlapping shaded region. Example 1:. Test …
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Advanced word problems often include a practical restriction: whole numbers, nonnegative values, capacity, budget, or minimum requirements. Example 1:. A truck can carry at most …
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Percent and rate inequalities require careful setup. Example 1 - tax:. After 8 percent tax, the total must be at most 54 dollars. Divide:. Example …
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For advanced inequalities, the final answer is only trustworthy if it passes a test. Checklist:. Did you flip the sign only when multiplying or dividing …
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Course Syllabus
This self-paced GED® Math course follows a 12-lesson sequence. Work through the modules in order so that each skill supports the next.
Course sequence
Module 1 - Lessons 1-4
- Advanced Inequality Mindset
- Interval Notation and Endpoint Logic
- Tough Linear Inequalities
- Compound Inequalities: AND and OR
Module 2 - Lessons 5-8
- Absolute Value Inequalities: Inside and Outside
- Quadratic Inequalities
- Sign Charts for Products
- Rational Inequalities
Module 3 - Lessons 9-12
- Systems of Inequalities
- Inequality Word Problems with Constraints
- Advanced Percent and Rate Inequalities
- Final Strategy: Test Regions and Check
Practice and completion
- Use worked examples and lesson practice to check understanding after each module.
- Review incorrect answers, explain the correction, and repeat weak skills.
- Complete the available mixed or final course practice to demonstrate readiness.
Course Outcomes
By the end of this course, learners will be able to:
- Explain and apply the mathematical ideas in Advanced Inequality Mindset.
- Solve multi-step problems involving Compound Inequalities: AND and OR and show a clear method.
- Interpret representations and check the reasonableness of work involving Sign Charts for Products.
- Choose efficient strategies for unfamiliar questions related to Systems of Inequalities.
- Combine skills from Final Strategy: Test Regions and Check with earlier topics in mixed practice.
- Use feedback and answer explanations to diagnose and correct mistakes.
- Complete mixed, exam-style practice with clearer reasoning and greater independence.
📝 Practice Questions
64 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.