An inequality is a mathematical statement that compares the values of two expressions using inequality symbols such as <, >, ≤, or ≥.

**Linear Inequalities:**These are inequalities that involve linear functions and are represented on the coordinate plane as lines or half-planes.**Absolute Value Inequalities:**These involve the absolute value of a variable and can be solved using the properties of absolute value.**Quadratic Inequalities:**These involve quadratic functions and can be solved using methods such as graphing, factoring, or the quadratic formula.

Inequalities are typically expressed using the following notation:

**<:**Less than**>:**Greater than**≤:**Less than or equal to**≥:**Greater than or equal to

To solve an inequality, follow these general steps:

**Isolate the variable:**Use inverse operations to get the variable on one side of the inequality.**Identify the solution set:**Determine the range of values for the variable that satisfy the inequality.**Graph the solution:**Represent the solution set on a number line or coordinate plane.

When studying inequalities, it's important to understand the properties of inequalities and how to solve them. Here are some key concepts to focus on:

- Understanding the meaning of the inequality symbols (<, >, ≤, ≥)
- Identifying the solution set for an inequality
- Graphing inequalities on a number line or coordinate plane
- Solving linear, absolute value, and quadratic inequalities using appropriate methods

Practice solving a variety of inequality problems to reinforce your understanding of the topic. Pay attention to any special cases or rules that apply to specific types of inequalities.

Remember to check your solutions by substituting the values back into the original inequality to ensure they satisfy the given conditions.

Good luck with your study of inequalities!

Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.