Solving radical inequalities Test

Front

What is a radical inequality?

Back

An inequality that contains a radical expression, such as √(x) or ∛(x).

Front

What does it mean to isolate the radical in an inequality?

Back

To rearrange the inequality so that the radical expression is on one side and all other terms are on the other side.

Front

What is the first step in solving a radical inequality with one radical?

Back

Isolate the radical symbol.

Front

When graphing an inequality, what does an open dot represent?

Back

An open dot indicates that the value at that point is not included in the solution set (used for < or >).

Front

What does a closed dot represent when graphing an inequality?

Back

A closed dot indicates that the value at that point is included in the solution set (used for ≤ or ≥).

Front

How do you solve the inequality √(8x-16) ≥ 4?

Back

1. Isolate the radical: √(8x-16) ≥ 4. 2. Square both sides: 8x - 16 ≥ 16. 3. Solve for x: x ≥ 4.

Front

What is the solution set for the inequality √(8x-16) ≥ 4?

Back

[4, +∞) - x must be greater than or equal to 4.

Front

What happens to the inequality symbol when you divide by a negative number?

Back

The inequality symbol flips direction.

Front

What is the importance of checking your solutions in radical inequalities?

Back

To ensure that the solutions satisfy the original inequality, as squaring both sides can introduce extraneous solutions.

Front

What is an extraneous solution?

Back

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