Evaluate 2^(3x+4)<2^(2x+8)

$2^{3 x + 4} < 2^{2 x + 8}$

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

$2^{3 x + 4} < 2^{2 x + 8}$

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

$3 x + 4 < 2 x + 8$

Solve for $x$ .

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

Subtract $2 x$ from both sides of the inequality.

$3 x + 4 - 2 x < 8$

Subtract $2 x$ from $3 x$ .

$x + 4 < 8$

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

Subtract $4$ from both sides of the inequality.

$x < 8 - 4$

Subtract $4$ from $8$ .

$x < 4$

The result can be shown in multiple forms.

Inequality Form:

$x < 4$

Interval Notation:

$(- \infty, 4)$