SAT Prep Lesson: Linear Inequalities
Learn to solve and graph linear inequalities on the number line step by step. Engage with SAT practice sets that test solution-set understanding. Master inequality concepts to boost your Math score.
Master the SAT with our targeted lesson on Linear Inequalities, part of SAT Sphere’s Digital SAT curriculum. This lesson delivers in-depth concept explanations, problem-solving techniques, and SAT-style practice questions to help you improve your SAT performance. Ideal for both SAT Math and Reading & Writing, each lesson helps you build confidence for test day.
SAT Topics Covered in the Linear Inequalities Lesson
This SAT Sphere lesson focuses on essential SAT test topics in the Linear Inequalities section. You'll build a strong understanding of core concepts, learn time-saving test-taking strategies, and apply your knowledge to realistic Digital SAT practice questions.
01
Introduction to Linear Inequalities
Frames the lesson goals and reminds students of required prior skills: solving one- and two-step linear equations, inverse operations, combining like terms, the distributive property, basic comparison symbols, and reading values on a number line.
02
Inequality Symbols and Solution Sets
Defines <, ≤, >, ≥, introduces interval notation, and explains that an inequality’s solution is a range of values—building on students’ earlier work with numeric comparisons in the Fundamentals module.
03
One-Step Inequalities: Addition and Subtraction
Teaches how to isolate the variable when a single add-or-subtract operation is present, refreshing the inverse-operation strategy first mastered in Basic Algebraic Operations.
04
One-Step Inequalities: Multiplication and Division
Shows how multiplying or dividing—especially by a negative—solves an inequality and flips its sign, extending the method from Slide 3 and reinforcing sign rules from earlier integer lessons.
05
Two-Step and Multi-Step Inequalities
Combines like terms, applies the distributive property, and performs two operations to isolate the variable—building on Slide 4 and the earlier ‘Two-Step Linear Equations’ lesson.
06
Compound Inequalities and Logical Connectors
Explores ‘and’/‘or’ statements, rewriting them as joined or split ranges, extending the multi-step skills from Slide 5.
07
Graphing Single Inequalities on a Number Line
Demonstrates open vs. closed circles and directional shading to visualize solutions—building on Slides 3–5 where solution ranges were obtained algebraically.
08
Graphing Compound Inequalities
Shows how to represent ‘and’/‘or’ ranges on a number line and connect disjoint intervals, extending Slide 6’s logical concepts and Slide 7’s graphing technique.
09
Modeling Word Problems with Inequalities
Translates real-world constraints into linear inequalities and interprets solutions, building on prior equation-modeling practice from the Linear Equations lesson.
10
Key Takeaways and Targeted Practice
Summarizes the inequality toolkit, highlights common SAT traps, and provides mixed practice to solidify understanding before moving on.
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Build Your Digital SAT Skills with the Fundamentals of Algebra Module
This lesson is part of the Fundamentals of Algebra module, a structured SAT prep unit designed to improve your performance in key areas of the Digital SAT. Each module includes multiple SAT-focused lessons that develop critical thinking, analytical skills, and test-taking confidence. Progress through each module to strengthen your understanding and raise your overall SAT score.
Explore More Digital SAT Lessons in the Fundamentals of Algebra Module
Advance your SAT preparation by completing other SAT Sphere lessons in the Fundamentals of Algebra module. Each lesson targets a specific concept tested on the Digital SAT, helping you deepen your knowledge and refine your skills for the real exam.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
Ratios and Proportions
Understanding and solving ratio problems. Setting up and solving proportions.
Introduction to Exponents and Powers
Understanding the laws of exponents. Simplifying expressions involving exponents.
Unit Conversion and Rates
Converting between units and solving problems involving rates. Applications in real-world contexts.
Roots and Radicals
Simplifying square roots and other radicals. Solving equations involving radicals.
Absolute Value
Working with absolute value equations and inequalities. Practical applications of absolute value in real-world problems.
Basic Algebraic Operations
Introduction to variables, constants, and coefficients. Understanding algebraic expressions and basic operations (addition, subtraction, multiplication, division).
Solving Linear Equations
Techniques for solving single-variable linear equations. Application of linear equations in word problems.
Percentages
Calculating percentages and solving percentage problems. Applications of percentages in various contexts.
Simplifying Algebraic Expressions
Techniques for combining like terms and using the distributive property. Simplifying complex algebraic expressions.
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