Question

Select the correct answer. What is the solution to this inequality? 3(1/4)^x+1<192

Answer 1

The solution to the exponential inequality is x < -4.

What is the exponential inequality?

The exponential inequality given in this problem is:

$3\left(\frac{1}{4}\right)^{x + 1} < 192$

Then:

$\left(\frac{1}{4}\right)^{x + 1} < \frac{192}{3}$

$\left(\frac{1}{4}\right)^{x + 1} < 64$

$\left(\frac{1}{4}\right)^{x + 1} < 4^3$

Applying the exponent property, we have that:

$4^3 = \left(\frac{1}{4}\right)^{-3}$

Hence:

$\left(\frac{1}{4}\right)^{x + 1} < \left(\frac{1}{4}\right)^{-3}$

$x + 1 < -3$

$x < -4$

The solution is is x < -4.

You can learn more about inequalities at https://brainly.com/question/18290022