Solve for x 7^(x-1)>49^x

$7^{x - 1} > 49^{x}$

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

$7^{x - 1} > 7^{2 x}$

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

$x - 1 > 2 x$

Solve for $x$ .

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

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

$x - 1 - 2 x > 0$

Subtract $2 x$ from $x$ .

$- x - 1 > 0$

Add $1$ to both sides of the inequality.

$- x > 1$

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

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

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

Simplify the left side.

Dividing two negative values results in a positive value.

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

Divide $x$ by $1$ .

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

Simplify the right side.

Divide $1$ by $- 1$ .

$x < - 1$

The result can be shown in multiple forms.

Inequality Form:

$x < - 1$

Interval Notation:

$(- \infty, - 1)$

Solve for x 7^(x-1)>49^x

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