Inequalities
Lessons in this chapter
About Inequalities
Inequalities is a short but essential extension of Linear Equations, replacing the equals sign with <, >, ≤, or ≥ and asking kids to solve for a range of values instead of one.
Solve linear inequalities uses the same inverse-operation moves from Linear Equations, undoing addition, subtraction, multiplication, or division on both sides, to isolate the variable, but the answer this time is a range like x > 5 rather than a single value like x = 5.
The one genuinely new rule this chapter introduces is what happens when multiplying or dividing both sides by a negative number: the inequality sign flips direction, so x/(−2) < 4 solves to x > −8, not x < −8, a step that has no equivalent in solving equations and is worth double-checking every time a negative appears.
The chapter's single lesson, Solve Linear Inequalities, is a 7th grade math worksheet worked in the page rather than a page of explanation. The math problems are marked as your child answers them, which matters here because the one rule that is easy to forget, flipping the inequality sign when multiplying or dividing by a negative, shows up as a wrong answer right where it happened. It is free to try, with no login needed for your first 3.
Frequently asked questions
Solve Linear Inequalities is the one lesson in this chapter. It treats an inequality much like the equations of the previous chapter, isolating the variable step by step, with the one difference that multiplying or dividing both sides by a negative number reverses the inequality sign. The solution is a range of values rather than a single answer. This sits in the Common Core domain Expressions and Equations (7.EE).
A linear inequality compares two expressions using <, >, ≤, or ≥ instead of an equals sign: x + 3 < 10 is an inequality, x + 3 = 10 is an equation. The equation has exactly one solution; the inequality is true for a whole range of values.
Isolate the variable using the same inverse operations as solving an equation: add, subtract, multiply, or divide both sides by the same amount. Solve Linear Inequalities works through both one-step cases (like x − 4 > 9) and multi-step cases that need simplifying first, the same progression Linear Equations followed.
Multiplying or dividing by a negative number reverses the order of every number on the number line: if 2 < 5, multiplying both sides by −1 gives −2 and −5, and −2 is actually greater than −5, not less. Flipping the inequality sign is what keeps the statement true after that reversal.
Solving correctly but forgetting to flip the sign: for example, solving −2x > 8 by dividing both sides by −2 and writing x > −4 instead of the correct x < −4. This is the single most common error in this chapter, precisely because it has no equivalent step in solving equations.
An equation’s answer is one specific value, like x = 8. An inequality’s answer is every value that makes the statement true: x > 5 includes 5.001, 6, 100, and every other number greater than 5, not just one of them.