If 2x+2(1−x)>3x−2>2x−5, then x can take which of the following values?
- A−2
- B2
- C4
- D−4
Solution & Step-by-step Explanation
Let's break down the compound inequality into two parts.
Part 1:
2x+2(1−x)>3x−2
2x+2−2x>3x−2
2>3x−2
4>3x⟹x<
3
4
≈1.33
Part 2:
3x−2>2x−5
3x−2x>−5+2
x>−3
Combining both parts, we get:
−3Among the given options:
A) −2 (lies within the interval)
B) 2 (does not lie within the interval)
C) 4 (does not lie within the interval)
D) −4 (does not lie within the interval)
Thus, x=−2.
Part 1:
2x+2(1−x)>3x−2
2x+2−2x>3x−2
2>3x−2
4>3x⟹x<
3
4
≈1.33
Part 2:
3x−2>2x−5
3x−2x>−5+2
x>−3
Combining both parts, we get:
−3
A) −2 (lies within the interval)
B) 2 (does not lie within the interval)
C) 4 (does not lie within the interval)
D) −4 (does not lie within the interval)
Thus, x=−2.