If 5x+5>2+2x and 5x+3≤4x+5, then x can take which of the following values?
- A3
- B−2
- C−3
- D1
Solution & Step-by-step Explanation
Let's solve the two inequalities separately:
First Inequality:
5x+5>2+2x
Subtract 2x from both sides:
3x+5>2
Subtract 5 from both sides:
3x>−3
Divide by 3:
x>−1
Second Inequality:
5x+3≤4x+5
Subtract 4x from both sides:
x+3≤5
Subtract 3 from both sides:
x≤2
Combining both results, the range of valid values for x is:
−1From the given choices:
Option A (3) is out of range.
Option B (−2) is out of range.
Option C (−3) is out of range.
Option D (1) satisfies the condition −1<1≤2.
First Inequality:
5x+5>2+2x
Subtract 2x from both sides:
3x+5>2
Subtract 5 from both sides:
3x>−3
Divide by 3:
x>−1
Second Inequality:
5x+3≤4x+5
Subtract 4x from both sides:
x+3≤5
Subtract 3 from both sides:
x≤2
Combining both results, the range of valid values for x is:
−1
Option A (3) is out of range.
Option B (−2) is out of range.
Option C (−3) is out of range.
Option D (1) satisfies the condition −1<1≤2.