If 5−3x<4−x and 5(2−x)>2−2x, then x can take which of the following values?
- A0
- B−1
- C1
- D3
Solution & Step-by-step Explanation
Solve the first inequality:
5−3x<4−x
5−4<3x−x
1<2x⟹x>0.5
Solve the second inequality:
5(2−x)>2−2x
10−5x>2−2x
10−2>5x−2x
8>3x⟹x<
3
8
≈2.67
Combining both conditions:
0.5Among the given options (0,−1,1,3), only x=1 satisfies this range.
5−3x<4−x
5−4<3x−x
1<2x⟹x>0.5
Solve the second inequality:
5(2−x)>2−2x
10−5x>2−2x
10−2>5x−2x
8>3x⟹x<
3
8
≈2.67
Combining both conditions:
0.5