Solve the Inequality for x 7^(3x)<49^(1-x)

$7^{3 x} < 49^{1 - x}$

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

$7^{3 x} < 7^{2 (1 - x)}$

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

$3 x < 2 (1 - x)$

Solve for $x$ .

Simplify $2 (1 - x)$ .

Apply the distributive property.

$3 x < 2 \cdot 1 + 2 (- x)$

Multiply.

Multiply $2$ by $1$ .

$3 x < 2 + 2 (- x)$

Multiply $- 1$ by $2$ .

$3 x < 2 - 2 x$

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

Add $2 x$ to both sides of the inequality.

$3 x + 2 x < 2$

Add $3 x$ and $2 x$ .

$5 x < 2$

Divide each term in $5 x < 2$ by $5$ and simplify.

Divide each term in $5 x < 2$ by $5$ .

$\frac{5 x}{5} < \frac{2}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} < \frac{2}{5}$

Divide $x$ by $1$ .

$x < \frac{2}{5}$

The result can be shown in multiple forms.

Inequality Form:

$x < \frac{2}{5}$

Interval Notation:

$(- \infty, \frac{2}{5})$