If 4+3x≤6+x and 3x+5>2+2x; then x can take which of the following values?

Let's solve both linear inequalities step by step:
First Inequality:

4+3x≤6+x
Subtract x from both sides:

4+2x≤6
Subtract 4 from both sides:

2x≤2
x≤1
Second Inequality:

3x+5>2+2x
Subtract 2x from both sides:

x+5>2
Subtract 5 from both sides:

x>−3
Combining both results, the range for x is:

−3Now let's check the given options to see which value falls inside this interval (−3,1]:

A) 2 (False, since 2>1)

B) −2 (True, since −3<−2≤1)

C) 4 (False, since 4>1)

D) −4 (False, since −4<−3)

Thus, x can take the value −2.