Solve the Inequality for x (1/3)^(x+4)>=(1/9)^x

${(\frac{1}{3})}^{x + 4} \geq {(\frac{1}{9})}^{x}$

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

${(\frac{1}{3})}^{x + 4} \geq {(\frac{1}{3})}^{2 x}$

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

$x + 4 \geq 2 x$

Solve for $x$ .

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

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

$x + 4 - 2 x \geq 0$

Subtract $2 x$ from $x$ .

$- x + 4 \geq 0$

Subtract $4$ from both sides of the inequality.

$- x \geq - 4$

Divide each term in $- x \geq - 4$ by $- 1$ and simplify.

Divide each term in $- x \geq - 4$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \leq \frac{- 4}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \leq \frac{- 4}{- 1}$

Divide $x$ by $1$ .

$x \leq \frac{- 4}{- 1}$

Simplify the right side.

Divide $- 4$ by $- 1$ .

$x \leq 4$

The solution consists of all of the true intervals.

$x \geq 4$

The result can be shown in multiple forms.

Inequality Form:

$x \geq 4$

Interval Notation:

$[4, \infty)$

Solve the Inequality for x (1/3)^(x+4)>=(1/9)^x

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