Question

0,75^2x+4>(4/3)^2-3x

Answer 1

$0.75^{2x+4}$> $( \frac{4}{3}) ^{2-3x}$
$( \frac{3}{4} ) ^{2x+4} > (\frac{4}{3}) ^{2-3x}$
$( \frac{4}{3}) ^{-2x-4}> (\frac{4}{3} ) ^{2-3x}$
-2x-4>2-3x

Answer 2

We can start by simplifying both sides of the inequality using the rules of exponents:

0.75^(2x+4) > (4/3)^2 - 3x

0.75^(2x) * 0.75^4 > 16/9 - 3x

0.5625 * 0.75^(2x) > 16/9 - 3x

Next, we can isolate the term with the variable on one side of the inequality and simplify:

0.5625 * 0.75^(2x) + 3x > 16/9

Multiply both sides of the inequality by 9 to get rid of the denominator on the right side:

5.0625 * 0.75^(2x) + 27x > 16

Finally, we can solve for x by subtracting 5.0625 * 0.75^(2x) from both sides and dividing by 27:

x > (16 - 5.0625 * 0.75^(2x)) / 27

Since the left side of the inequality is always positive, we know that the right side must also be positive for the inequality to hold. Therefore, we can use a numerical method or a graphing calculator to approximate the range of values of x that satisfy the inequality.