Solve the Inequality for x 2^(4x+1)<=512

$2^{4 x + 1} \leq 512$

Step 1

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

$2^{4 x + 1} \leq 2^{9}$

Step 2

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

$4 x + 1 \leq 9$

Step 3

Solve for $x$ .

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

Subtract $1$ from both sides of the inequality.

$4 x \leq 9 - 1$

Subtract $1$ from $9$ .

$4 x \leq 8$

Divide each term in $4 x \leq 8$ by $4$ and simplify.

Divide each term in $4 x \leq 8$ by $4$ .

$\frac{4 x}{4} \leq \frac{8}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} \leq \frac{8}{4}$

Divide $x$ by $1$ .

$x \leq \frac{8}{4}$

Simplify the right side.

Divide $8$ by $4$ .

$x \leq 2$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 2$

Interval Notation:

$(- \infty, 2]$

Step 5