Radical Inequalities and Solution Sets

The video tutorial covers solving radical inequalities, highlighting the differences from solving radical equations. It provides a step-by-step procedure for solving these inequalities, including isolating variables, squaring both sides, and considering the domain of expressions under radicals. Three examples are worked through in detail, demonstrating the process and the importance of checking conditions for the domain. The tutorial emphasizes the use of number lines to visualize solutions and the overlap of conditions.

What is the first step in solving a radical inequality?

• Isolate the radical expression

• Multiply both sides by a constant

• Add a constant to both sides

• Subtract a constant from both sides

In the first example, what is the inequality after isolating the radical?

• 3x - 6 ≥ 9

• 3x - 6 ≤ 9

• 3x - 6 ≥ 3

• 3x - 6 ≤ 3

What must be true about the expression under a radical?

• It must be less than zero

• It must be less than or equal to zero

• It must be greater than zero

• It must be greater than or equal to zero

What is the solution set for the first example?

• x is between 2 and 5, inclusive

• x is between 2 and 5, exclusive

• x is greater than 5

• x is less than 2

In the second example, what is the inequality after squaring both sides?

• x - 3 = 5 - x

• x - 3 ≤ 5 - x

• x - 3 ≥ 5 - x

• x - 3 < 5 - x

What is the domain condition for x - 3 in the second example?

• x ≥ 3

• x < 3

• x ≤ 3

• x > 3

What is the solution set for the second example?

• x is between 3 and 5, inclusive

• x is between 4 and 5, inclusive

• x is greater than 5

• x is less than 3

In the third example, what is the inequality after isolating the radical?

• x + 5 ≥ 2.5 - √(x + 10)

• x + 5 = 2.5 - √(x + 10)

• x + 5 > 2.5 - √(x + 10)

• x + 5 < 2.5 - √(x + 10)

What is the domain condition for x + 5 in the third example?

• x ≤ -5

• x < -5

• x > -5

• x ≥ -5

What is the solution set for the third example?

• x is less than -79/16

• x is greater than -79/16

• x is between -5 and 0

• x is between -10 and -5