Algebra Examples

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

Step 1

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

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

Step 2

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

$2 \cdot 2 \geq x + 1$

Step 3

Solve for $x$ .

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Step 3.1

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

$x + 1 \leq 2 \cdot 2$

Step 3.2

Multiply $2$ by $2$ .

$x + 1 \leq 4$

Step 3.3

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

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Step 3.3.1

Subtract $1$ from both sides of the inequality.

$x \leq 4 - 1$

Step 3.3.2

Subtract $1$ from $4$ .

$x \leq 3$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x \leq 3$

Interval Notation:

$(- \infty, 3]$

Step 5