Solving Square Root Inequalities

The video tutorial covers solving square root inequalities, starting with basic principles and moving through several examples of increasing complexity. It emphasizes the importance of isolating the square root, considering the domain restrictions, and using a number line test to verify solutions. The tutorial concludes with a discussion on why some inequalities have no solution.

What is the first step in solving square root inequalities?

• Square both sides

• Multiply both sides by a negative number

• Take the reciprocal of both sides

• Add a constant to both sides

Why must x - 4 be non-negative in the inequality x - 4 ≤ 25?

• Because it simplifies the equation

• Because square roots of negative numbers are not real

• Because x must be a positive number

• Because it makes the inequality easier to solve

What is the purpose of the number line test in solving inequalities?

• To find the exact solution

• To verify the solution range

• To eliminate extraneous solutions

• To simplify the inequality

What is the solution to the inequality 2x + 1 ≥ 16?

• x ≥ 7.5

• x ≤ 7.5

• x ≤ 8

• x ≥ 8

Why is it important to test different zones on a number line?

• To ensure all possible solutions are considered

• To verify the inequality is correct

• To find the midpoint of the solution

• To eliminate negative solutions

What happens to the inequality sign when dividing by a negative number?

• It becomes an equality

• It flips direction

• It stays the same

• It is removed

What is the solution to the inequality -2√(x + 1) < -8?

• x > 15

• x ≤ 15

• x < 15

• x ≥ 15

Why does the inequality √x < -3 have no solution?

• Because square roots cannot be negative

• Because x must be negative

• Because the inequality is invalid

• Because it results in a complex number