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Maths Exercices
Absolute Value Inequalities

Solve absolute value inequalities

Solve for v.

|v + 8| ≤ 2

Look at the inequality.

|v + 8| ≤ 2

Since v + 8 can be either positive or negative, split the inequality into two cases.

positive

or negative

v + 8 ≤ 2
 
-(v + 8) ≤ 2

First, solve the positive case.

v + 8 ≤ 2

 
v ≤ -6
Subtract 8 from both sides

Next, solve the negative case.

-(v + 8) ≤ 2

 
- v - 8 ≤ 2

Apply the distributive property

- v ≤ 10

Add 8 to both sides

v ≥ -10
Multiply both sides by -1 and reverse the direction of the inequality symbol

Now, see if the two inequalities can be combined into a single statement. The variable v is greater than or equal to - 10 and less than or equal to - 6, which means it is in between the two values. Write the solution as a single statement.

-10 ≤ v ≤ -6 


Solve for l.

-8|l| > -40

Solution: l