Why does absolute value have two answers

Ross Millikan Ross Millikan k 26 26 gold badges silver badges bronze badges. Sign up or log in Sign up using Google. Sign up using Facebook. Sign up using Email and Password. Post as a guest Name. Email Required, but never shown. Featured on Meta. Now live: A fully responsive profile. Related 0. If we plug this one into the equation we get,.

We get the same number on each side but with opposite signs. This will happen on occasion when we solve this kind of equation with absolute values. Now, before we check each of these we should give a quick warning. We only exclude a potential solution if it makes the portion without absolute value bars negative.

In this case both potential solutions will make the portion without absolute value bars positive and so both are in fact solutions. Both sides of the equation contain absolute values and so the only way the two sides are equal will be if the two quantities inside the absolute value bars are equal or equal but with opposite signs. Or in other words, we must have,. Both with be solutions provided we solved the two equations correctly. However, it will probably be a good idea to verify them anyway just to show that the solution technique we used here really did work properly.

In the case the quantities inside the absolute value were the same number but opposite signs. If one side does not contain an absolute value then we need to look at the two potential answers and make sure that each is in fact a solution.

Add 5 to each term:. Divide each term by Problem 9. Subtract 1 from each term:. The sense will change. That is,. This is the form of the solution, for any argument a :. For which values of x will this be true? Problem For example, if. What is the geometrical meaning of each of the following? And therefore what values has x? For example, the number 9 is 9 units away from 0.

Therefore its absolute value is 9. The number -9 is the same distance from zero, so its absolute value is also just 9. In both cases the magnitude, or absolute value, of your number is just plain old "9" because you've removed any negative sign that might have existed. Taking absolute value of a number leaves a positive unchanged, and makes a negative positive. An absolute value is written like this: x , and is read as "the absolute value of x.

Another use of the absolute value bars is actually to force a number to be negative, by writing - x. This takes the number, makes it positive, and then negates it.