Solving Absolute Value Inequalities

The video tutorial covers solving inequalities, graphing them, and understanding absolute value equations. It explains how to handle cases with no solution or all real numbers and differentiates between disjunction and conjunction in inequalities. The tutorial provides step-by-step guidance on solving these mathematical problems, emphasizing the importance of understanding the symbols and operations involved.

What is the first step in solving the inequality 3m + 9 > -9(3n + 5)?

• Add 9 to both sides

• Divide by 3

• Subtract 3m from both sides

• Distribute the -9 across the parentheses

When distributing a negative sign, what must you remember to do?

• Ignore the negative sign

• Only apply it to the first term

• Add it to the outside of the parentheses

• Apply it to all terms inside the parentheses

What is the result of solving the inequality 3n + 5 < 0?

• n < -5/3

• n = -5/3

• n > -5/3

• n > 5/3

How do you graph the inequality 7M > 5?

• Shade the region to the left of M = 5

• Draw a line at M = 5

• Shade the region to the right of M = 5

• Draw a line at M = 7

What is the solution to the inequality 7M < 14?

• M = 2

• M > 2

• M < 2

• M < 7

What is the first step in solving an absolute value equation?

• Multiply both sides by 2

• Isolate the absolute value expression

• Add all terms to one side

• Subtract the constant term

How many cases must you consider when solving an absolute value equation?

• One

• Two

• Three

• Four

What is the first step in solving the equation |x + 3| = 7?

• Multiply both sides by 7

• Write two separate equations

• Subtract 3 from both sides

• Add 3 to both sides

What is the solution to the equation |x - 5| = 0?

• No solution

• x = 5

• x = 0

• x = -5

What is the solution to the inequality |x + 1| = 0?

• No solution

• x = 1

• x = -1

• x = 0