Precalculus : Inequalities and Linear Programming
Study concepts, example questions & explanations for Precalculus
All Precalculus Resources
Example Questions
Example Question #1 : Solve Absolute Value Inequalities
Solve the following inequality:
First we need to get the expression with the absolute value sign by itself on one side of the inequality. We can do this by subtracting two from both sides then dividing everything by three.
Since absolute value signs make both negative and positive values positive we need to set up a double inequality.
Now to solve for 
Example Question #7 : Linear Inequalities
Solve for 
If 
a) 
Even if we didn't know the rule about flipping the inequality, this answer makes sense - for example, 
b) 
Example Question #1 : Solve Absolute Value Inequalities
Solve the absolute value inequality.
First, simplify so that the absolute value function is by itself on one side of the inequality.
Note that the symbol flipps when you divide both sides by 
Next, the two inequalities that result after removing the absolute value symbols are
When you simplify the two inequalities, you get
Thus, the solution is
Example Question #41 : Inequalities And Linear Programming
To solve absolute value inequalities, you have to write it two different ways. But first, divide out the 4 on both sides so that there is just the absolute value on the left side. Then, write it normally, as you see it: 
Example Question #842 : Pre Calculus
Solve the following:
To solve absolute value inequalities create two functions.
Simply remember that when solving inequalities with absolute values, you keep one the same and then flip the sign and inequality on the other.
Thus,
Then, you must write it in interval notation.
Thus,
Certified Tutor
Certified Tutor
All Precalculus Resources
