Quick Answer
A linear inequality is a mathematical statement using symbols like < or > to compare two algebraic expressions. On the Digital SAT, these appear frequently in the Math section, typically as multiple-choice or student-produced response questions. Mastering these is essential for solving word problems and interpreting shaded regions on a coordinate plane.
A linear inequality is an inequality that involves a linear function, typically expressed in the form ax + b < c (or using >, ≤, or ≥), where x is a variable and a, b, and c are constants. Unlike equations, these represent a range of possible solutions rather than a single discrete value.
Question: If 3x - 5 > 10, what is the smallest integer value of x? Solution: 1. Add 5 to both sides: 3x > 15. 2. Divide by 3: x > 5. 3. Since x must be strictly greater than 5, the smallest integer value is 6.
Forgetting to flip the sign: Students often forget to reverse the direction of the inequality symbol when multiplying or dividing both sides by a negative number.
Misinterpreting 'at most' or 'at least': Students frequently swap the symbols for 'less than or equal to' and 'greater than or equal to' when translating word problems.
Confusing solid and dashed lines: On graphing questions, students may fail to distinguish between strict inequalities (dashed lines) and non-strict inequalities (solid lines).
Students targeting 750+ should know that when solving systems of linear inequalities, you can often test specific 'corner points' or coordinates from the answer choices to quickly eliminate regions that do not satisfy all given constraints, saving valuable time on complex word problems.
A linear inequality on the SAT is a mathematical expression that relates two linear quantities using inequality symbols such as less than, greater than, or equal to. These concepts are fundamental to the Heart of Algebra section of the Digital SAT. They test your ability to determine a range of solutions and represent those solutions either algebraically or graphically on a coordinate plane.
To solve a linear inequality, you follow the same basic algebraic steps as solving a linear equation, such as isolating the variable using inverse operations. However, you must remember the critical rule: if you multiply or divide both sides of the inequality by a negative number, you must flip the direction of the inequality sign to maintain the mathematical truth of the statement.
The primary difference is that a linear equation represents a specific set of values where two expressions are equal, whereas a linear inequality represents a range of values where one expression is greater or less than another. Graphically, a linear equation is represented by a line, while a linear inequality is represented by a shaded region on one side of a boundary line.
Linear inequalities typically appear in approximately 3 to 5 questions per SAT exam, spanning across both Math modules. These questions range from simple algebraic manipulation to complex word problems involving systems of inequalities. Because they are a foundational topic, they are highly likely to appear in some form on every Digital SAT administration.
