Solving Math Inequalities Step by Step

Welcome to understanding inequalities! Today we'll learn how to compare numbers in mathematics.Let's start by learning the four main inequality symbols.Now let's see how these inequalities look on a number line.Let's look at some real-world examples where we use inequalities.Now that we understand what inequalities are and how they work, we're ready to learn how to solve them.Let's explore the fundamental rules for solving inequalities.There are three key rules we need to remember when solving inequalities.Let's solve our first example: two x plus three is greater than seven.First, we subtract three from both sides to isolate the term with x.Next, we divide both sides by two. Since two is positive, the inequality direction stays the same.Now let's solve an example with a negative coefficient: negative three x plus two is greater than or equal to eight.First, subtract two from both sides.Now comes the crucial step. When we divide by negative three, we must reverse the direction of the inequality.Let's try one more example: four x minus five is greater than eleven.Now let's solve some complex inequalities with variables on both sides.Let's solve this step by step, starting with three x minus four is less than two x plus five.Our solution shows x is less than nine. Let's graph this on a number line.Let's solve another complex inequality: four x plus two is less than or equal to negative two x plus ten.We'll solve this step by step, being careful with our operations.Our solution shows x is less than or equal to four thirds. Let's graph this solution.Let's verify our first solution by testing some values.Let's review the key points for solving complex inequalities.Thanks for learning about complex inequalities with Spark.E!