Solve the Inequality for x 4^(3x+2)<64

$4^{3 x + 2} < 64$

Step 1

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

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

Step 2

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

$3 x + 2 < 3$

Step 3

Solve for $x$ .

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

Subtract $2$ from both sides of the inequality.

$3 x < 3 - 2$

Subtract $2$ from $3$ .

$3 x < 1$

Divide each term in $3 x < 1$ by $3$ and simplify.

Divide each term in $3 x < 1$ by $3$ .

$\frac{3 x}{3} < \frac{1}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} < \frac{1}{3}$

Divide $x$ by $1$ .

$x < \frac{1}{3}$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{1}{3}$

Interval Notation:

$(- \infty, \frac{1}{3})$

Step 5