(Lesson 5-4) Solving Radical Equations and Inequalities

Front

What is a radical equation?

Back

An equation that contains a variable within a radical (square root, cube root, etc.).

Front

How do you isolate a radical in an equation?

Back

To isolate a radical, you can move all other terms to the opposite side of the equation.

Front

What is the first step in solving the equation 3 + √(3x + 12) ≤ 9?

Back

Subtract 3 from both sides to isolate the radical: √(3x + 12) ≤ 6.

Front

What is the importance of squaring both sides of an equation when solving radical equations?

Back

Squaring both sides eliminates the radical, but it can introduce extraneous solutions that must be checked.

Front

What does the solution set [-4, 8] represent in the context of the inequality 3 + √(3x + 12) ≤ 9?

Back

It represents all values of x that satisfy the inequality, including -4 and 8.

Front

How do you check for extraneous solutions in radical equations?

Back

Substitute the potential solutions back into the original equation to verify if they hold true.

Front

What is the solution to the inequality √(3x - 2) > 13?

Back

The solution is (57, +∞), meaning x must be greater than 57.

Front

What does the notation (57, +∞) indicate?

Back

It indicates that x can take any value greater than 57, but not including 57 itself.

Front

What is the significance of the cube root in the inequality ∛(x + 1) < 2?

Back

It indicates that the expression x + 1 must be less than 8, leading to the solution x < 7.

Front

How do you solve the inequality 2√(x - 6) + 1 < 9?

Back

First, isolate the radical: 2√(x - 6) < 8, then divide by 2: √(x - 6) < 4.