(Q19) Sample #1, Math 141/146 common final, "less than" situation

TL;DR

Learn how to solve and graph absolute value inequalities, finding the values of x that satisfy the inequality.

Transcript

for number 19 we are going to solve and graph absolute value of 9x - 1 is less than 17 notice that this absolute value is already isolated for us that's good and especially we have less than two a positive number so that's good all right let's think about how this is going to work and let's set out the questions correctly because we have to take ou... Read More

Key Insights

• #️⃣ Absolute value inequalities compare the absolute value of a quantity with a positive number.
• 🟠 When graphing absolute value inequalities, open circles indicate the boundary points, and shading represents the valid range of values.
• 🫱 To solve absolute value inequalities, isolate the absolute value, set up separate inequalities for the positive and negative versions of the right-hand side, and solve each inequality independently.

Questions & Answers

Q: How do you solve and graph absolute value inequalities?

To solve an absolute value inequality, isolate the absolute value term and create two separate inequalities. On a number line, plot the two boundary points and shade the region between them to represent the solution set.

Q: What does it mean when the inequality is "less than" in absolute value inequalities?

When the inequality is "less than," the absolute value of the expression inside should be between the negative and positive values of the right-hand side of the inequality.

Q: How do you remove the absolute value from an inequality?

To remove the absolute value from an inequality, set up separate inequalities for both the positive and negative versions of the right-hand side. Then, solve each inequality independently.

Q: Can you reduce fractions in the solutions of absolute value inequalities?

Yes, if there are fractions in the solutions of absolute value inequalities, you can simplify them by reducing them to lowest terms if possible.

Summary & Key Takeaways

• Absolute value inequalities compare the absolute value of a quantity with a positive number.

• To solve and graph an absolute value inequality, identify the range of values that satisfy the inequality.

• Use a number line to represent the possible values of x and shade the region between the two boundary points.