GED® Algebra: Inequalities and Graphing
A focused GED® Algebra course on inequalities. Students learn inequality symbols, number-line graphs, one-step and two-step inequalities, the sign flip rule, variables on both sides, fraction and decimal inequalities, compound and absolute value inequalities, word-problem modeling, and linear inequalities in two variables. Lessons include many examples, and every practice answer gives detailed step-by-step reasoning.
📚 Course Curriculum
An inequality compares two expressions that are not necessarily equal. Instead of one answer, an inequality often has many possible answers. The symbols:. \(<\): less …
Open trial session →A number-line graph shows all possible answers. [[figure:number_line_ineq An open circle means the endpoint is not included; the ray points toward the solution values.]]. Use …
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One-step inequalities solve almost like one-step equations. Example 1:. Subtract 7 from both sides:. Example 2:. Add 4 to both sides:. Example 3:. Divide by …
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Here is the special rule that makes inequalities different from equations:. When you multiply or divide both sides by a negative number, flip the inequality …
Open trial session →Two-step inequalities usually look like:. Subtract 5:. Divide by \(-1\) and flip:. Check by testing one value. For \(x<3\), try \(x=0\):. is true, so the …
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Multi-step inequalities need the same cleanup routine as equations. Use this order:. Distribute. Combine like terms. Move variables and constants. Divide by the coefficient. Flip …
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When variables appear on both sides, simplify first. Then collect variable terms on one side. Example 1:. Subtract \(2x\):. Add 3:. Divide:. Example 2:. Subtract …
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Fractions and decimals do not change the inequality rules. They only make the arithmetic heavier. Example 1:. Multiply every term by the LCD, 6:. Combine:. …
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A compound inequality joins two inequalities. AND means the number must satisfy both conditions:. This means numbers below 2 and numbers above 5 are included, …
Open trial session →Absolute value means distance from zero. Absolute value inequalities are about distance from a center. Less than means inside the distance:. means \(x\) is within …
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Use inequalities when a story says at least, at most, no more than, fewer than, under, over, minimum, or maximum. Example 1 - budget:. A …
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Some inequalities use both \(x\) and \(y\). Their solutions are points, not just numbers. Example:. To test whether \((1,4)\) is a solution, substitute \(x=1\) and …
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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
- What an Inequality Means
- Graphing Inequalities on a Number Line
- One-Step Inequalities
- The Sign-Flip Rule
Module 2 - Lessons 5-8
- Two-Step Inequalities
- Multi-Step Inequalities
- Variables on Both Sides
- Fraction and Decimal Inequalities
Module 3 - Lessons 9-12
- Compound Inequalities
- Absolute Value Inequalities
- Word Problems with Inequalities
- Linear Inequalities in Two Variables
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 What an Inequality Means.
- Solve multi-step problems involving The Sign-Flip Rule and show a clear method.
- Interpret representations and check the reasonableness of work involving Variables on Both Sides.
- Choose efficient strategies for unfamiliar questions related to Compound Inequalities.
- Combine skills from Linear Inequalities in Two Variables 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
62 interactive questions with instant feedback and explanations.
Enroll for free to unlock the full practice bank after the trial sessions.