How To Solve Absolute Value Inequalities, Basic Introduction, Algebra

TL;DR

Learn how to solve absolute value inequalities by writing two equations, changing the sign and direction of the inequality, and plotting the solutions on a number line.

Transcript

now what if we have an absolute value expression with an inequality what do we need to do well we still need to write two equations the first one is going to remain the same now for the second one we need to do two things we need to change the positive five to a negative five and we need to change the direction of the inequality so that's important... Read More

Key Insights

• 🤘 Absolute value inequalities require writing two equations, changing the sign and direction for the second equation.
• 😚 Solutions of absolute value inequalities are plotted on a number line, using open or closed circles and shading towards the right or left.
• 😑 Expressing the solution using interval notation provides a concise representation of the possible values of x.

Questions & Answers

Q: How do you solve absolute value inequalities?

To solve absolute value inequalities, write two equations, change the sign and direction of the inequality, plot the solutions on a number line, and express the solution using interval notation.

Q: What are the steps for solving absolute value inequalities?

The steps for solving absolute value inequalities include writing two equations, changing the sign and direction of the inequality, plotting the solutions on a number line, and expressing the solution using interval notation.

Q: Why is it important to change the sign and direction of the inequality in the second equation?

Changing the sign and direction in the second equation is crucial because it accounts for the absolute value expression. By doing so, we accurately represent the possible range of x that satisfies the inequality.

Q: How is the solution for absolute value inequalities represented on a number line?

The solution for absolute value inequalities is represented on a number line by plotting open or closed circles at the appropriate values of x and shading towards the right or left of these points, depending on the inequality.

Summary & Key Takeaways

• When solving absolute value inequalities, write two equations - one remains the same, and for the other, change the sign and direction of the inequality.

• Plot the solutions on a number line by determining the values of x that satisfy the inequalities.

• Express the solution using interval notation, which indicates the range of values for x.