Solving Radical Inequalities

Front

What is a radical inequality?

Back

An inequality that involves a variable within a radical (square root) expression.

Front

How do you isolate the radical in a radical inequality?

Back

To isolate the radical, you need to move all other terms to the opposite side of the inequality.

Front

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

Back

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

Front

What is the next step after isolating the radical in the inequality √(3x + 12) ≤ 6?

Back

Square both sides to eliminate the radical: 3x + 12 ≤ 36.

Front

How do you solve the inequality 3x + 12 ≤ 36?

Back

Subtract 12 from both sides: 3x ≤ 24, then divide by 3: x ≤ 8.

Front

What is the solution set for the inequality 3 + √(3x + 12) ≤ 9?

Back

The solution set is [-4, 8].

Front

What is the domain of the function √(x - 6)?

Back

The domain is x ≥ 6, since the expression under the square root must be non-negative.

Front

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

Back

Subtract 1 from both sides: 2√(x - 6) < 8, then divide by 2: √(x - 6) < 4.

Front

What do you do after isolating the radical in the inequality √(x - 6) < 4?

Back

Square both sides: x - 6 < 16.

Front

What is the solution to the inequality x - 6 < 16?

Back

Add 6 to both sides: x < 22.