If $3x-4>2-\frac{x}{3}$ and $3x+5>4x-5$, then find the value of $x$ from the options?

Let's solve the two inequalities separately:First Inequality:
$$3x-4>2-\frac{x}{3}$$
$$3x+\frac{x}{3}>2+4$$
$$\frac{9x+x}{3}>6$$
$$\frac{10x}{3}>6$$
$$10x>18⟹x>1.8$$
Second Inequality:
$$3x+5>4x-5$$
$$5+5>4x-3x$$
$$10>x⟹x<10$$
Combining both inequalities, the range for $x$ is:
$$1.8<x<10$$
Now check the given options to see which value falls inside this interval $(1.8,10)$:A) 7 (Valid, because $1.8<7<10$)B) 10 (Invalid, since $x<10$)C) -11 (Invalid)D) 1 (Invalid)Hence, $x=7$ is the correct answer choice.