If 2+2x<5−
2
x
and 5x+3>5−5x, then x can take which of the following values?
- A2
- B0
- C-2
- D1
Solution & Step-by-step Explanation
Let's solve the two inequalities separately:
First Inequality:
2+2x<5−
2
x
2x+
2
x
<5−2
2
5x
<3
5x<6⟹x<1.2
Second Inequality:
5x+3>5−5x
5x+5x>5−3
10x>2
x>
10
2
⟹x>0.2
Combining both inequalities, we get the range for x:
0.2From the given options:
A) 2 (Incorrect, 2>1.2)
B) 0 (Incorrect, 0<0.2)
C) -2 (Incorrect, −2<0.2)
D) 1 (Correct, since 0.2<1<1.2)
Thus, x can take the value 1.
First Inequality:
2+2x<5−
2
x
2x+
2
x
<5−2
2
5x
<3
5x<6⟹x<1.2
Second Inequality:
5x+3>5−5x
5x+5x>5−3
10x>2
x>
10
2
⟹x>0.2
Combining both inequalities, we get the range for x:
0.2
A) 2 (Incorrect, 2>1.2)
B) 0 (Incorrect, 0<0.2)
C) -2 (Incorrect, −2<0.2)
D) 1 (Correct, since 0.2<1<1.2)
Thus, x can take the value 1.