Answer:
Explanation:
To solve the inequality |2x+5|<0.5, we need to consider two cases: when the expression inside the absolute value is positive and when it is negative.
Case 1: 2x+5 is positive:
If 2x+5 is positive, then the absolute value of 2x+5 is equal to 2x+5 itself. Therefore, we have the inequality 2x+5<0.5.
To solve this inequality, we can subtract 5 from both sides:
2x<0.5-5
2x<-4.5
Now, divide both sides by 2:
x<-4.5/2
x<-2.25
So, in this case, the solution to the inequality is x<-2.25.
Case 2: 2x+5 is negative:
If 2x+5 is negative, then the absolute value of 2x+5 is equal to -(2x+5). Therefore, we have the inequality -(2x+5)<0.5.
To solve this inequality, we can multiply both sides by -1 (which changes the direction of the inequality):
2x+5>-0.5
Now, subtract 5 from both sides:
2x>-0.5-5
2x>-5.5
Finally, divide both sides by 2:
x>-5.5/2
x>-2.75
So, in this case, the solution to the inequality is x>-2.75.
Combining the solutions from both cases, we have x<-2.25 or x>-2.75.
Therefore, the solution to the inequality |2x+5|<0.5 is x<-2.25 or x>-2.75.