all right the first problem we're going to tackle in math 136 is solving an absolute value equation so here we have nine minus the absolute value of nine x equals eight and we have the steps already written out on the right side of the screen so the first step is get the absolute value all by itself so what's stopping the absolute value from being all by itself right the absolute value here is in blue and then we still have a 9 that's on the left side of the equation with the absolute value and we have a minus so it's 9 minus first thing we're going to get rid of is the nine so to get rid of a positive 9 we're going to subtract 9 from both sides of the equation and 9 minus nine is zero they cancel because 0 plus anything doesn't change that anything so we're going to be left with negative the absolute value of nine x equals 8 minus 9 is negative one now we have to get rid of the negative sign so we still have the negative sign out in front that's really a negative one that's multiplying our absolute value to get rid of multiplication by negative one we're going to divide both sides by negative one and here the negative that negative on the outside divided by a negative cancels and so what we are left with is the absolute value of 9x equals positive one so we are now done the absolute value is all by itself on the left side of the equation so now what we're going to do is we're going to split up the absolute value we're on step two so when you split it up you're going to have one side where it's positive meaning that the one on the right side is going to be positive so all we do is drop the absolute value signs 9x equals one and the other side we make the negative we make the one negative so it's going to be 9 x equals negative 1. and then all we need to do is in each equation because now we have two equations we solve for actually solving means get it by itself on one side of the equation so we've got 9 times x it's 9x means Nine's times x to get rid of multiplication by nine we're going to divide both sides by nine so X is going to equal 1 9. that's one possible answer and the other answer we get from the second equation which is 9x equals negative one to get rid of multiplication by nine we divide by nine again x equals negative 1 9. okay so what we're going to do now is we're actually going to enter our answers in MyMathLab okay so we should be looking at MyMathLab now we need to put in positive 1 9 and negative 1 9. so we're going to put 1 divided by 9 and then a little trick is going to Arrow over to the right you Arrow over to the right so that when you put your comma it's not in the denominator and then we want negative 1 divided by 9. okay so this is nice clean we check our answer and we got it that's it right there