An equation is a mathematical statement that shows the equality of two expressions. To solve an equation, you need to find the value of the variable that makes the equation true.

A linear equation is an equation of the form ax + b = c, where a, b, and c are constants, and x is the variable. To solve a linear equation, isolate the variable on one side of the equation by performing inverse operations.

A quadratic equation is an equation of the form ax^2 + bx + c = 0, where a, b, and c are constants, and x is the variable. To solve a quadratic equation, you can use methods like factoring, completing the square, or using the quadratic formula.

An inequality is a mathematical statement that shows the relationship between two expressions, where one is greater than, less than, greater than or equal to, or less than or equal to the other.

A linear inequality is an inequality of the form ax + b < c or ax + b > c, where a, b, and c are constants, and x is the variable. To solve a linear inequality, you can use similar methods as solving linear equations, but you also need to consider the direction of the inequality sign.

A quadratic inequality is an inequality of the form ax^2 + bx + c < 0 or ax^2 + bx + c > 0. To solve a quadratic inequality, you can use techniques such as graphing or testing intervals to determine the solution set.

- Practice solving equations and inequalities of different types to familiarize yourself with various problem-solving methods.
- Understand the properties of equality and inequality, such as the addition and multiplication properties, which allow you to perform operations on both sides of an equation or inequality.
- Pay attention to special cases when solving equations and inequalities, such as division by zero or taking the square root of both sides.
- Use visual aids and graphs to understand the solutions to inequalities, especially quadratic inequalities.
- Review the steps for solving different types of equations and inequalities to build a strong problem-solving approach.

Study GuideEquations and Inequalities Worksheet/Answer key

Equations and Inequalities Worksheet/Answer key

Equations and Inequalities Worksheet/Answer key

Equations and Inequalities Worksheet/Answer keyMultistep Equations Worksheet/Answer keyInequalities Worksheet/Answer keyGraphing Inequalities

Algebra (NCTM)

Represent and analyze mathematical situations and structures using algebraic symbols.

Use symbolic algebra to represent situations and to solve problems, especially those that involve linear relationships.

Recognize and generate equivalent forms for simple algebraic expressions and solve linear equations

Grade 7 Curriculum Focal Points (NCTM)

Number and Operations and Algebra: Developing an understanding of operations on all rational numbers and solving linear equations

Students extend understandings of addition, subtraction, multiplication, and division, together with their properties, to all rational numbers, including negative integers. By applying properties of arithmetic and considering negative numbers in everyday contexts (e.g., situations of owing money or measuring elevations above and below sea level), students explain why the rules for adding, subtracting, multiplying, and dividing with negative numbers make sense. They use the arithmetic of rational numbers as they formulate and solve linear equations in one variable and use these equations to solve problems. Students make strategic choices of procedures to solve linear equations in one variable and implement them efficiently, understanding that when they use the properties of equality to express an equation in a new way, solutions that they obtain for the new equation also solve the original equation.