Solve the Inequality for x 25^2>=5^(x+1)

$25^{2} \geq 5^{x + 1}$

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

$5^{2 \cdot 2} \geq 5^{x + 1}$

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

$2 \cdot 2 \geq x + 1$

Solve for $x$ .

Rewrite so $x$ is on the left side of the inequality.

$x + 1 \leq 2 \cdot 2$

Multiply $2$ by $2$ .

$x + 1 \leq 4$

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

Subtract $1$ from both sides of the inequality.

$x \leq 4 - 1$

Subtract $1$ from $4$ .

$x \leq 3$

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$