Solve the following in equation and represent the solution set on the number line
3x/5+ 2 < x + 4 ≤ x/2+5,x€R
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Given : 3x/5+ 2 < x + 4 ≤ x/2+5
To find : solution set
Solution:
3x/5+ 2 < x + 4 ≤ x/2+5
3x/5+ 2 < x + 4
multiplying both sides by 5
=> 3x + 10 < 5x + 20
Subtract 3x + 20 from both sides
=> - 10 < 2x
Divide by sides by 2
=> - 5 < x
x + 4 ≤ x/2+5
=> 2x + 8 ≤ x + 5
=> x ≤ - 3
Combining both
- 5 < x ≤ - 3
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