Like what you saw?
Create FREE Account and:
 Watch all FREE content in 21 subjects(388 videos for 23 hours)
 FREE advice on how to get better grades at school from an expert
 Attend and watch FREE live webinar on useful topics
Absolute Value Equations  Problem 3
Alissa Fong
Alissa Fong
MA, Stanford University
Teaching in the San Francisco Bay Area
Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts
Some absolute value equations may start off equaling a negative value, but before concluding that the equation has no solution, first isolate the absolute value equation to see how many, if any, solutions there will be. Remember that if the absolute value quantity is equal to a negative number, then there is no solution to the equation since an absolute value cannot equal a negative number. The first thing to do when solving an absolute value equation is to isolate the absolute value quantity using the same rules that apply to isolating the variable in an equation. In other words, eliminate everything else on the same side of the equal sign except for the absolute value quantity using inverse operations. Next, split the equation into two equations and remove the absolute value signs. One equation should be equal to the positive quantity on the other side, and the second equation should be equal to the negative quantity. However, if the quantity equals 0, then there will only be one equation to solve. Don't forget to check your solutions by substituting them back into the original equation.
A lot of students when they see a problem like this they think ohoh! No solution because an absolute value can't be equal to a negative number. You can't have a negative distance. However, the absolute value has to be isolated before you look to see if there's going to be zero solutions or one solution or two solutions.
Like in this case I can't tell anything about how many answers I'll have until I get the absolute value by itself. So I'm going to have to add 4 to both sides and I'll have absolute value of 2x plus 3 equals to 0. Now since it's equal to 0 I know I'm only going to have one solution so it gets a little bit easier like when I'm separating this absolute value, I can't have something equal to 0 and also equal to 0 like what's 0? 2x minus 3 equals 0? Whatever, you don't even have to do that problem. My problem is just the extension here 2x plus 3 equals 0. Subtract 3 from both sides so you'll have 2x equals 3, divide both sides by 2 and you get x equals 3/2.
Again keep in mind x can be a negative number because I'm going to absolute valueize it after I multiply by 2 and add 3.
Please enter your name.
Are you sure you want to delete this comment?
Alissa Fong
M.A. in Secondary Mathematics, Stanford University
B.S., Stanford University
Alissa has a quirky sense of humor and a relatable personality that make it easy for students to pay attention and understand the material. She has all the math tips and tricks students are looking for.
Your tutorials are good and you have a personality as well. I hope you have more advanced college level stuff, because I like the way you teach.”
Thanks alot for such great lectures... I never found learning this easier ever before... keep up the great work.... :)”
You seem so kind, it's awesome. Easier to learn from people who seem to be rooting for ya!' thanks”
Concept (1)
Sample Problems (9)
Need help with a problem?
Watch expert teachers solve similar problems.

Absolute Value Equations
Problem 1 12,269 viewsSolve for x.
3x − 4 = 12 
Absolute Value Equations
Problem 2 9,805 viewsSolve for x.
2x − 3 + 3= 5 
Absolute Value Equations
Problem 3 8,036 viewsSolve for x.
2x + 3 − 4 = 4 
Absolute Value Equations
Problem 4 7,242 viewsSolve for x.
2x + 1 + 10 = 3 
Absolute Value Equations
Problem 5 508 views 
Absolute Value Equations
Problem 6 470 views 
Absolute Value Equations
Problem 7 318 views 
Absolute Value Equations
Problem 8 315 views 
Absolute Value Equations
Problem 9 307 views
Comments (0)
Please Sign in or Sign up to add your comment.
·
Delete