Graphing Inequalities: A Simple Guide

Welcome to our lesson on inequality symbols and number lines!Let's start by learning the four main inequality symbols.These symbols help us compare numbers and show their relationships on a number line.For strict inequalities like x greater than 3, we use an open circle to show the starting point is not included.For inclusive inequalities like x less than or equal to negative two, we use a closed circle to show the point is included.Let's practice with more examples. For each inequality, we'll mark the number line appropriately.To solve a linear inequality, we follow similar steps as solving equations, but with special attention to the inequality sign.First, we subtract 4 from both sides to isolate the term with x.Then we divide both sides by 2 to solve for x.To graph this inequality, we first plot the line x equals 3.Since our inequality is less than, we use a dashed line and shade the left side.Now let's solve an inequality with a negative coefficient: negative three x plus 2 is less than or equal to 5.After subtracting 2 from both sides, we get negative three x is less than or equal to 3.Here's the special rule: when dividing by a negative number, we must flip the inequality sign.For this inequality, x is greater than or equal to negative one.Since it's greater than or equal to, we use a solid line and shade the right side.Now we'll explore how to graph and solve systems of inequalities.Here's our system of inequalities. We'll graph each one separately, then find their overlap.For y greater than 2x plus 1, we first draw the line, then shade above it since the inequality symbol is greater than.For y less than negative one-half x plus 3, we draw the line and shade below it.To verify our shading, let's test the point (0,0) in both inequalities.Let's look at a practical example: planning a party with budget and time constraints.The overlapping region in purple shows all possible combinations of guests and activities that satisfy both our budget and time constraints.Let's review what we've learned about systems of inequalities.Thanks for learning about systems of inequalities with Spark.E!