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 inequalities?

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 solution back into the original equation to see if it holds true.

Front

What is the solution to the inequality 2√(x - 6) + 1 < 9?

Back

The solution is [6, 22).

Front

What does the notation ( -∞, 12 ) mean in interval notation?

Back

It represents all real numbers less than 12.

Front

What is the significance of the domain when solving radical equations?

Back

The domain must be considered to ensure that the expressions under the radicals are non-negative.

Front

What is an extraneous solution?

Back

A solution that emerges from the process of solving an equation but does not satisfy the original equation.