If $4+3x\le 6+x$ and $3x+5>2+2x$, then $x$ can take which of the following values?

We need to solve the system of two linear inequalities.First Inequality:
$$4+3x\le 6+x$$
Subtract $x$ from both sides:
$$4+2x\le 6$$
Subtract $4$ from both sides:
$$2x\le 2$$
$$x\le 1\text{— (Equation 1)}$$
Second Inequality:
$$3x+5>2+2x$$
Subtract $2x$ from both sides:
$$x+5>2$$
Subtract $5$ from both sides:
$$x>-3\text{— (Equation 2)}$$
Combining both conditions from Equation 1 and Equation 2:
$$-3<x\le 1$$
Now let's check the given options to see which value falls inside this interval $(-3,1]$:Option A: $2$ (False, as $2>1$)Option B: $-2$ (True, as $-3<-2\le 1$)Option C: $4$ (False, as $4>1$)Option D: $-4$ (False, as $-4<-3$)Therefore, $x$ can take the value $-2$.