In this Grade 8 lesson from Saxon Math, Course 3, students learn how to write and solve inequalities, then graph their solution sets on a number line using open and closed circles to indicate excluded and included values. The lesson covers translating word problems into inequality notation, solving multi-step inequalities such as 3x + 1 ≤ 7 by applying inverse operations, and representing continuous solution sets with shaded regions and arrows. Students also practice verifying their solution sets by testing values inside and outside the graphed region.
Section 1
📘 Graphing Solutions to Inequalities on a Number Line
An inequality is a mathematical statement used to indicate a range of possible numbers. Letting represent a possible number, we write
This card just sets the stage. Next, you’ll work through examples on solving inequalities and graphing their solutions on a number line.
Section 2
Graphing inequalities on a number line
An inequality shows a range of possible values. Use an open circle to show a number is excluded (like with or ) and a solid, filled-in circle to show a number is included (like with or ). The shaded part of the number line represents the entire solution set of possible numbers.
Think of it as a VIP party guest list! An open circle means that number didn't get an invite, but all the numbers nearby did. A solid circle means that number is the guest of honor and is definitely included! The shaded line is the dance floor where all the cool, invited numbers hang out.
Section 3
Solving Two-Step Inequalities
Solve an inequality just like an equation by using inverse operations to isolate the variable. Whatever you do to one side, you must do to the other to keep it balanced. For example, to solve , you first subtract 1 from both sides, then divide both sides by 3.
Solving an inequality is like being a secret agent on a mission to isolate the variable 'x'! First, you have to get rid of any sidekicks hanging around by adding or subtracting. Then, if 'x' has a coefficient partner, you divide to uncover its true identity. Just follow the steps to crack the code!
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Section 1
📘 Graphing Solutions to Inequalities on a Number Line
An inequality is a mathematical statement used to indicate a range of possible numbers. Letting represent a possible number, we write
This card just sets the stage. Next, you’ll work through examples on solving inequalities and graphing their solutions on a number line.
Section 2
Graphing inequalities on a number line
An inequality shows a range of possible values. Use an open circle to show a number is excluded (like with or ) and a solid, filled-in circle to show a number is included (like with or ). The shaded part of the number line represents the entire solution set of possible numbers.
Think of it as a VIP party guest list! An open circle means that number didn't get an invite, but all the numbers nearby did. A solid circle means that number is the guest of honor and is definitely included! The shaded line is the dance floor where all the cool, invited numbers hang out.
Section 3
Solving Two-Step Inequalities
Solve an inequality just like an equation by using inverse operations to isolate the variable. Whatever you do to one side, you must do to the other to keep it balanced. For example, to solve , you first subtract 1 from both sides, then divide both sides by 3.
Solving an inequality is like being a secret agent on a mission to isolate the variable 'x'! First, you have to get rid of any sidekicks hanging around by adding or subtracting. Then, if 'x' has a coefficient partner, you divide to uncover its true identity. Just follow the steps to crack the code!
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter