Create equivalent expressions in the equation that all have equal bases.

Since the bases are the same, then two expressions are only equal if the exponents are also equal.

Move all terms containing to the left side of the inequality.

Subtract from both sides of the inequality.

Subtract from .

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

Add to both sides of the inequality.

Add and .

The solution consists of all of the true intervals.

The result can be shown in multiple forms.

Inequality Form:

Interval Notation:

Solve for x (1/2)^(3x-1)<(1/2)^(2x+1)