How To Solve Absolute Value Equations Basic Introduction Algebra

what is the absolute value of five and what is the absolute value of negative eight the absolute value of five is five the absolute value of negative eight is positive eight the absolute value cannot produce negative result it will always produce positive result or if you have 0 it will give you 0. now let's say if you have an equation for example the absolute value of is equal to seven what are the possible values of can equal two things seven or negative seven because if you plug these numbers in the equation will be true the absolute value of seven is seven so this works the absolute value of negative seven is also seven so could be seven or negative seven both will make the equation true so now how can we use this to solve typical problem that involves an absolute value symbol so let's say if we have the function the absolute value of plus 2 is equal to 9. how can we solve this equation well the first thing you should do is write two equations the original one and another one where the inside function is equal to negative nine instead of positive nine and solve for both so in the first one we can see that can be equal to seven and for the second one is equal to negative eleven so these are the solutions find the value of given this equation so just like the last example let's set 2x minus 5 equal to 1 and negative one so first let's add five one plus five is six and then let's divide both sides by two so is equal to three and in the other example let's add five to both sides negative 1 plus 5 is 4 and then divide by 2 is 2. so if you check the work you can see that it's going to work out so if we plug in two two times two is four four minus five is negative one the absolute value of negative one is one so the equation is true now if we plug in three it should also work two times three is equal to six six minus five is one the absolute value of one is one so that works now what about this one the absolute value of five minus one is equal to negative 2. what's the solution the absolute value function can never equal negative number so there's no solution for this particular example it can only equal zero or positive number now let's try one more example for this particular lesson find the value of now what you don't want to do is write this equation on the left is equal to 7 or negative 7. first you want to modify the equation you want to get the absolute value function by itself so let's add 2 first so we're going to get 9 on the right side next let's divide by 3. now you want the absolute value symbol by itself on one side once you have it at this point now you want to write two equations so the first one's gonna be minus one is equal to three and the second minus one is equal to negative three so if we add one is equal to four and if we add one to the other one negative three plus one is negative two so this is the solution