Let's first simplify the absolute values in the inequality.

0.5(3+4|𝑥−5|) < 0.3(2-3|𝑥-5|)

Next, distribute the constants on both sides of the inequality.

1.5 + 2|𝑥-5| < 0.6 - 0.9|𝑥-5|

Now, let's isolate the absolute value term on one side of the inequality.

2.5 + 2|𝑥-5| < -0.9|𝑥-5|

Subtract 2.5 from both sides:

2|𝑥-5| < -3.4|𝑥-5|

Now, divide both sides by 2 to isolate the absolute value on one side:

|𝑥-5| < -1.7|𝑥-5|

Absolute value is always non-negative, so the inequality |𝑥-5| < -1.7|𝑥-5| is not possible.

Thus, there is no solution to the original inequality 0.5(3+4|𝑥−5|) < 0.3(2-3|𝑥-5|).