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Solve each inequality |2x+5|<0.5

User Brechmos
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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.

User Gregory Lancaster
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