Solve for x (1/16)^(2x-10)<=(1/16)^(3x+13)

${(\frac{1}{16})}^{2 x - 10} \leq {(\frac{1}{16})}^{3 x + 13}$

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

${(\frac{1}{16})}^{2 x - 10} \leq {(\frac{1}{16})}^{3 x + 13}$

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

$2 x - 10 \leq 3 x + 13$

Solve for $x$ .

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

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

$2 x - 10 - 3 x \leq 13$

Subtract $3 x$ from $2 x$ .

$- x - 10 \leq 13$

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

Add $10$ to both sides of the inequality.

$- x \leq 13 + 10$

Add $13$ and $10$ .

$- x \leq 23$

Divide each term in $- x \leq 23$ by $- 1$ and simplify.

Divide each term in $- x \leq 23$ by $- 1$ . When multiplying or dividing both sides of an inequality by a negative value, flip the direction of the inequality sign.

$\frac{- x}{- 1} \geq \frac{23}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} \geq \frac{23}{- 1}$

Divide $x$ by $1$ .

$x \geq \frac{23}{- 1}$

Simplify the right side.

Divide $23$ by $- 1$ .

$x \geq - 23$

The solution consists of all of the true intervals.

$x \leq - 23$

The result can be shown in multiple forms.

Inequality Form:

$x \leq - 23$

Interval Notation:

$(- \infty, - 23]$

Solve for x (1/16)^(2x-10)<=(1/16)^(3x+13)

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