Radical Inequalities and Their Solutions

The video tutorial explains how to solve radical inequalities, focusing on an example where the inequality is rad x + 3 - 2 ≤ 9. It begins by determining the minimum x value by ensuring the expression under the radical is non-negative. The tutorial then solves the original inequality, finding the range of valid x values. Various x values are tested to confirm the solution, concluding that x must be between -3 and 118 inclusive. The video emphasizes understanding the properties of radicals and inequalities.

What is a radical inequality?

• An equation with a variable in the exponent

• An equation with a variable in the denominator

• An equation with a variable under a radical

• An equation with a variable in the numerator

Why must the expression under a radical be non-negative?

• Because radicals are undefined

• Because radicals are always zero

• Because radicals cannot be negative

• Because radicals can only be positive

What is the minimum value of x for the inequality rad(x + 3) ≥ 0?

• -1

• -3

• 0

• 3

What is the range of x for the inequality rad(x + 3) - 2 ≤ 9?

• x ≥ -3 and x ≤ 118

• x ≥ 0 and x ≤ 118

• x ≥ -3 and x ≤ 18

• x ≥ 0 and x ≤ 18

Which of the following values is NOT a solution to the inequality rad(x + 3) - 2 ≤ 9?

• 118

• 0

• 120

• -3

What happens when you test the value x = -10 in the inequality?

• It results in a negative radical

• It results in a positive radical

• It satisfies the inequality

• It results in zero

What is the result of testing x = 118 in the inequality?

• It results in zero

• It satisfies the inequality

• It results in a negative radical

• It does not satisfy the inequality

What is the conclusion about the range of x for the inequality?

• x must be greater than 0 and less than 118

• x must be greater than or equal to 0 and less than or equal to 118

• x must be greater than or equal to -3 and less than or equal to 118

• x must be greater than -3 and less than 118