Solve the Inequality for x 10^x>100^(-2x-5)

$10^{x} > 100^{- 2 x - 5}$

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

$10^{x} > 10^{2 (- 2 x - 5)}$

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

$x > 2 (- 2 x - 5)$

Solve for $x$ .

Simplify $2 (- 2 x - 5)$ .

Apply the distributive property.

$x > 2 (- 2 x) + 2 \cdot - 5$

Multiply.

Multiply $- 2$ by $2$ .

$x > - 4 x + 2 \cdot - 5$

Multiply $2$ by $- 5$ .

$x > - 4 x - 10$

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

Add $4 x$ to both sides of the inequality.

$x + 4 x > - 10$

Add $x$ and $4 x$ .

$5 x > - 10$

Divide each term in $5 x > - 10$ by $5$ and simplify.

Divide each term in $5 x > - 10$ by $5$ .

$\frac{5 x}{5} > \frac{- 10}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} > \frac{- 10}{5}$

Divide $x$ by $1$ .

$x > \frac{- 10}{5}$

Simplify the right side.

Divide $- 10$ by $5$ .

$x > - 2$

The result can be shown in multiple forms.

Inequality Form:

$x > - 2$

Interval Notation:

$(- 2, \infty)$