To remove the radical on the left side of the inequality, square both sides of the inequality.

Multiply the exponents in .

Apply the power rule and multiply exponents, .

Cancel the common factor of .

Cancel the common factor.

Rewrite the expression.

Simplify.

Raise to the power of .

Move all terms not containing to the right side of the inequality.

Add to both sides of the inequality.

Add and .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Set the radicand in greater than or equal to to find where the expression is defined.

Solve for .

Divide each term by and simplify.

Divide each term in by .

Cancel the common factor of .

Cancel the common factor.

Divide by .

Divide by .

Add to both sides of the inequality.

The domain is all values of that make the expression defined.

Use each root to create test intervals.

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is less than the right side , which means that the given statement is always true.

True

True

Test a value on the interval to see if it makes the inequality true.

Choose a value on the interval and see if this value makes the original inequality true.

Replace with in the original inequality.

The left side is not less than the right side , which means that the given statement is false.

False

False

Compare the intervals to determine which ones satisfy the original inequality.

True

False

True

False

The solution consists of all of the true intervals.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Solve for X square root of 2a-6<4