Solve the Inequality for x 5^(2x)<125^(x-5)

$5^{2 x} < 125^{x - 5}$

Step 1

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

$5^{2 x} < 5^{3 (x - 5)}$

Step 2

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

$2 x < 3 (x - 5)$

Step 3

Solve for $x$ .

Simplify $3 (x - 5)$ .

Apply the distributive property.

$2 x < 3 x + 3 \cdot - 5$

Multiply $3$ by $- 5$ .

$2 x < 3 x - 15$

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

Subtract $3 x$ from both sides of the inequality.

$2 x - 3 x < - 15$

Subtract $3 x$ from $2 x$ .

$- x < - 15$

Divide each term in $- x < - 15$ by $- 1$ and simplify.

Divide each term in $- x < - 15$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} > \frac{- 15}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} > \frac{- 15}{- 1}$

Divide $x$ by $1$ .

$x > \frac{- 15}{- 1}$

Simplify the right side.

Divide $- 15$ by $- 1$ .

$x > 15$

Step 4

The result can be shown in multiple forms.

Inequality Form:

$x > 15$

Interval Notation:

$(15, \infty)$

Step 5

Solve the Inequality for x 5^(2x)<125^(x-5)

Related Questions

Support LCMGCF.com by disabling your adblocker.