Solve for x 5^x>25^(x+1)

$5^{x} > 25^{x + 1}$

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

$5^{x} > 5^{2 (x + 1)}$

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

$x > 2 (x + 1)$

Solve for $x$ .

Simplify $2 (x + 1)$ .

Apply the distributive property.

$x > 2 x + 2 \cdot 1$

Multiply $2$ by $1$ .

$x > 2 x + 2$

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

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

$x - 2 x > 2$

Subtract $2 x$ from $x$ .

$- x > 2$

Divide each term in $- x > 2$ by $- 1$ and simplify.

Divide each term in $- x > 2$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} < \frac{2}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} < \frac{2}{- 1}$

Divide $x$ by $1$ .

$x < \frac{2}{- 1}$

Simplify the right side.

Divide $2$ by $- 1$ .

$x < - 2$

The result can be shown in multiple forms.

Inequality Form:

$x < - 2$

Interval Notation:

$(- \infty, - 2)$

Solve for x 5^x>25^(x+1)

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