Solving Equations and Inequalities

Equations

An equation is a mathematical statement that shows that two expressions are equal. When solving an equation, the goal is to find the value of the variable that makes the equation true.

Steps for Solving Equations:

Use the properties of equality to isolate the variable on one side of the equation.
Perform the same operations on both sides of the equation to maintain equality.
Check your solution by substituting it back into the original equation.

Inequalities

An inequality shows a relationship between two expressions, indicating that one is less than, greater than, or not equal to the other. When solving an inequality, the goal is to find the set of values that make the inequality true.

Steps for Solving Inequalities:

Use the properties of inequality to isolate the variable on one side of the inequality.
Perform the same operations on both sides of the inequality, but remember to reverse the inequality sign if multiplying or dividing by a negative number.
Write the solution set in interval notation or as an inequality, depending on the context of the problem.

Study Guide

When studying how to solve equations and inequalities, it's important to understand the properties of equality and inequality, as well as the various techniques for isolating the variable and solving for its value. Practice working through different types of equations and inequalities, including linear, quadratic, and absolute value equations, as well as linear and compound inequalities. Focus on understanding the steps involved in solving each type of equation or inequality, and be sure to check your solutions to verify their accuracy.

Additionally, familiarize yourself with interval notation and the concept of solution sets for inequalities. Work through plenty of practice problems to reinforce your understanding and improve your problem-solving skills.

Remember to review any specific rules or exceptions related to solving particular types of equations or inequalities, such as special cases involving absolute value or inequalities with fractions or rational expressions.

Lastly, seek out additional resources such as online tutorials, textbooks, and worksheets to supplement your learning and gain more exposure to different problem-solving scenarios.