GED® Algebra: Advanced Equations & Applications
A harder follow-up to GED® Algebra: Equations Mastery. This course gives students advanced equation practice with more examples: nested parentheses, fractions and decimals, variables on both sides, literal equations, percent and rate applications, absolute value, proportions, quadratics, systems, radicals, and exponential equations. Every practice answer explains the solution step by step and names the likely trap.
📚 Course Curriculum
Hard equations are usually built from easy moves in a longer chain. The secret is not speed; it is order. Use this routine:. Clear grouping …
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Some equations have more than one layer of grouping. Work from the inside outward, or distribute carefully one layer at a time. Example 1:. Inside …
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Fractions are not a different kind of algebra. They only make the arithmetic heavier. To simplify, multiply every term by the least common denominator (LCD). …
Open trial session →Decimal equations often appear in money, tax, discount, interest, and percent problems. You can solve with decimals directly or rewrite them as fractions. Example 1:. …
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When variables appear on both sides, first simplify each side. Then collect variables. Example 1:. Distribute:. Subtract \(5x\):. Add 12:. Divide:. Example 2:. Add \(2x\) …
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A literal equation asks you to solve for a variable while other letters remain in the answer. Treat the other letters like numbers. Example 1:. …
Open trial session →Advanced word problems often compare two expressions. Example 1 - two plans:. Plan A costs 20 dollars plus 5 dollars per month. Plan B costs …
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Absolute value means distance from zero, so it cannot be negative. Most absolute value equations split into two cases. Example 1:. Two cases:. Solve:. Example …
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A proportion says two ratios are equal. You can often cross-multiply. Example 1:. Cross-multiply:. Divide:. Example 2:. Cross-multiply:. Divide by 10:. So:. Example 3:. Multiply …
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A quadratic equation has an \(x^2\) term. Many GED®-level quadratics can be solved by factoring or square roots. Example 1:. Take the square root of …
Open trial session →A system of equations asks for values that make two equations true at the same time. Example 1 - substitution:. Set the two expressions for …
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Some advanced equations use square roots, cubes, or exponents. The same inverse-operation idea still works. Example 1:. Square both sides:. Subtract 5:. Check:. Example 2:. …
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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 Equation Routine
- Parentheses Inside Parentheses
- Fractions: Clear the Denominators
- Decimals and Percent Equations
Module 2 - Lessons 5-8
- Variables on Both Sides: Harder Cases
- Literal Equations and Rearranging Formulas
- Word Problems with Two Expressions
- Absolute Value Equations
Module 3 - Lessons 9-12
- Proportions and Rational Equations
- Quadratic Equations
- Systems as Advanced Equations
- Radical and Exponential Equations
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 Equation Routine.
- Solve multi-step problems involving Decimals and Percent Equations and show a clear method.
- Interpret representations and check the reasonableness of work involving Word Problems with Two Expressions.
- Choose efficient strategies for unfamiliar questions related to Proportions and Rational Equations.
- Combine skills from Radical and Exponential Equations 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
60 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.