Those are not very interesting equations, its not very interesting when there are no variables inside the absolute value. The ones which are not are known as extraneous solutions. Solving absolute value equations kuta software llc. When solving equations with absolute value we can end up with more than one possible answer. In the above example, you would solve 2x 3 2 x and 2x 3 2 x. The only additional key step that you need to remember is to separate the original absolute value equation into two parts. I am currently in a pre calculus class at my high school. Absolute value equations and inequalities 10 if the symbol is 0 r. Absolute value equations with extraneous solutions thread starter pempem. Acces pdf extraneous solutions absolute value equations extraneous solutions absolute value equations this is likewise one of the factors by obtaining the soft documents of this extraneous solutions absolute value equations by online. An inequality is a mathematical statement that compares algebraic expressions using greater than, less than 2.
Some of the solutions of problem b may be solutions of the original problem, but some may not. So, either these equations absolute value of 5 equals x or absolute value of negative 5 equals x would have the single solution x equals 5. Even though the numbers 5 and 5 are different, they do have something in common. In the example above, we would get answers of x53 and x1. How to solve radical equations with extraneous solutions. A radical equation is an equation that contains a square root, cube root, or other higher root of the variable in the original problem. So when we are solving these problems, we must consider two scenarios, one where the value is positive and one where the value is negative. This course is designed for the student that wants to learn everything they will need to know about absolute value equations and inequalities. It gets more interesting when we put variables inside the absolute value.
It is great for sequential problems, such as solving equations. Use your description to write two linear equations that represent the solutions of the absolute value equation. I have build this portion very carefully using increasing levels of difficulty. When the absolute value is equal to zero, there is a single solution because zero is its own opposite. I have found that many students learn the procedure of solving absolute value inequalities without really understanding why they work. I have come across the concept of extraneous solutions, particularly when solving absolute value equations, radical equations, and logarithmic equations.
Free absolute value equation calculator solve absolute value equations with all the steps. Absolute value equations worksheet 2 here is a another 16 problem multiple choice worksheet where you will determine the solutions to equations containing absolute value. Before look at the worksheet, if you would like to know the basic stuff about solving absolute value equations, to download solving absolute value. Solving absolute value equations and inequalities she. It implies that every absolute value equation has an extraneous root. Worksheet given in this section will be much useful for the students who would like to practice problems on solving absolute value equations. Type in any equation to get the solution, steps and graph. High school math solutions quadratic equations calculator, part 1. Therefore, it cannot be a root of the original equation.
So, for example, j5j 5 and j 5j 5, since each is 5 units from 0 on the number line. Absolute value equations worksheet 1 pdf view answers. An extraneous solution is an apparent solution that must be rejected because it does not satisfy the original equation. X4 or x radical, rational, and absolute value equations joseph lee metropolitan community college. Solving absolute value equations is as easy as working with regular linear equations. The absolute value of a number is the number of units it is from 0 on the. The final problems deal with absolute value equations that may have extraneous solutions. Absolute value equations worksheet 1 rtf absolute value equations worksheet 1 pdf view answers. Absolute value equations and inequalities absolute value definition the absolute value of x, is defined as. Absolute value equations with extraneous solutions. But 2 is excluded from the domain of the original equation because it would make the denominator of one of the fractions zeroand division by zero is not allowed.
Absolute value equations and inequalities activity free. To solve absolute value equations, we must understand that the absoute value function makes a value positive. An extraneous solution is a solution that emerges from the process of solving the problem, but is not a valid solution to the original problem. Therefore, you must check all solutions in the original equation when you solve radical equations.
Radical equations with extraneous solutions worksheet. Below is the general approach on how to break them down into two equations. Absolute value equations and inequalities absolute value equations absolute value of a numberits distance from zero on the number line and distance is nonnegative absolute value equations can have 0, 1, or 2 solutions example 1solving absolute value equations quick check 1 remember to isolate absolute value get it by itself. Absolute value equations with extraneous solutions b solving equations with.
Absolute value functions is embedded in algebra 2, precalculus, calculus, act and sat. Once they have looked at the graphical solutions to a variety of absolute value equations with and without extraneous solutions, we will move on to inequalities. You might not require more period to spend to go to the book foundation as well as search for them. They are the same distance from 0 on the number line, but in opposite directions. An extraneous solution is a solution derived from an equation that is not a solution of the original equation. How are absolute value equations like linear equations. Eleventh grade lesson absolute value equations betterlesson. You should check each solution by plugging them into the given equation. Here we are going to see some practice questions on radical equations with extraneous solutions. This website uses cookies to ensure you get the best experience.