If 4x−5(2x−1)>2x+3>2−3x; then x can take which of the following values?
- A1
- B0
- C2
- D-3
Solution & Step-by-step Explanation
We can solve this system of linear inequalities by splitting it into two separate inequalities.
Part 1:
4x−5(2x−1)>2x+3
4x−10x+5>2x+3
−6x+5>2x+3
5−3>2x+6x
2>8x⟹x<
8
2
⟹x<0.25
Part 2:
2x+3>2−3x
2x+3x>2−3
5x>−1⟹x>−
5
1
⟹x>−0.2
Combining both results:
−0.2Let's test the given options to see which value falls in this range:
Option A) 1: Does not fall in the range.
Option B) 0: Since −0.2<0<0.25, 0 satisfies the condition.
Option C) 2: Does not fall in the range.
Option D) −3: Does not fall in the range.
Part 1:
4x−5(2x−1)>2x+3
4x−10x+5>2x+3
−6x+5>2x+3
5−3>2x+6x
2>8x⟹x<
8
2
⟹x<0.25
Part 2:
2x+3>2−3x
2x+3x>2−3
5x>−1⟹x>−
5
1
⟹x>−0.2
Combining both results:
−0.2
Option A) 1: Does not fall in the range.
Option B) 0: Since −0.2<0<0.25, 0 satisfies the condition.
Option C) 2: Does not fall in the range.
Option D) −3: Does not fall in the range.