Solving Absolute Value Inequalities

This video tutorial explains how to solve absolute value inequalities, including graphing solutions on a number line and using interval notation. It covers compound inequalities, trap questions, and scenarios with no solutions. The video also discusses cases where all real numbers are solutions and provides an advanced example to highlight key lessons in solving inequalities.

What should you do first when solving an absolute value inequality?

• Graph the solution

• Combine like terms

• Isolate the variable

• Write two inequalities

When you have a 'greater than' symbol in an absolute value inequality, what type of expression do you use?

• And

• Or

• Xor

• Not

What is the first step in solving the inequality |2x + 5| > 11?

• Subtract 5 from both sides

• Write two inequalities

• Add 5 to both sides

• Divide by 2

How do you represent the solution of |2x + 5| > 11 on a number line?

• Shade between -3 and 8

• Shade to the left of -8 and to the right of 3

• Shade between -8 and 3

• Shade to the right of -3 and to the left of 8

In the inequality |3x - 4| ≤ 17, what is the first step after writing the two inequalities?

• Multiply by 3

• Divide by 3

• Add 4 to both sides

• Subtract 4 from both sides

What does the solution of |3x - 4| ≤ 17 look like on a number line?

• Shade between -4 and 7

• Shade to the left of -4 and to the right of 7

• Shade between -7 and 4

• Shade to the right of -4 and to the left of 7

What is the solution to the inequality |3x + 5| < -3?

• All real numbers

• No solution

• x < -3

• x > 3

What is the solution to the inequality |4x - 3| > -4?

• x < -4

• x > 4

• No solution

• All real numbers

What should you do before writing two inequalities when solving |7x + 4| > 12?

• Add 4 to both sides

• Isolate the absolute value expression

• Subtract 4 from both sides

• Divide by 7

What is the solution to the inequality |7x + 4| > 12?

• x < 0 and x > 8/7

• x > 0 and x < 8/7

• x > 0 or x < 8/7

• x < 0 or x > 8/7