Original subtitles

hey it's professor Dave let's learn

about absolute values in our haste to

get through algebra there's one topic we

didn't mention so before we move on

let's quickly cover absolute values it's

important to know what these are

and how to graph them so let's become

familiar with this definition the

absolute value of any real number X

which is denoted by these little bracket

type things is the distance from zero to

that number on a number line

take the number three this is three

units away from zero so the absolute

value of 3 is 3 now look at negative 3

this is also 3 units away from zero so

the absolute value of negative 3 is 3

that brings us to a more practical

definition of absolute value as being

the magnitude of a number disregarding

its sign positive numbers are unchanged

by taking the absolute value while

negative numbers simply drop the

negative sign and become positive this

applies not just to integers but all

real numbers whether rational or

irrational absolute values obey

properties just like other operations so

we can see that the absolute value of a

B can be split up into the product of

two absolute values and the same goes

for division however let's note that the

absolute value of a plus B does not

equal the absolute value of a plus the

absolute value of B which we can

demonstrate with the values 1 and

negative 1 we clearly don't get the same

thing when we encounter absolute values

while solving equations it just adds

another step if we have the absolute

value of x equals 2 that means X could

be 2 or negative 2 so there are two

solutions to this equation if we try a

trickier one like the absolute value of

2x minus 1 equals 5 then again we split

this up into two equations it could

either be the case that 2x minus 1

equals 5 or 2x minus 1 could equal

negative 5 because once we take the

absolute value we get 5 either way that

means we now have to solve both of these

equations to get the two possible values

of X for the first one we add 1/2 and x

equals 3 for the other we do the same

thing but we get x equals negative 2 so

those are the two solutions in this case

the equations can get harder than this

but the approach will always be the same

the last thing we want to do is look at

simple graphs with absolute values we

know that a graph of y equals x will

look like this the x and y values and

every single point are equal to one

another and it's just a line with a

slope of 1 and a y-intercept of 0 now

what if we want to graph y equals the

absolute value of x well as we said all

positive values remain unchanged so

everything from the y axis to the right

will be just like it is now but negative

values will have their signs reversed

when we plug in negative 1 for X we

don't get negative 1 for y we get

positive 1 negative 2 gives us positive

2 and so forth that means that

everything to the left of the y axis or

all the negative inputs for X will be

reflected across the x axis so that we

get the positive versions of all these Y

values resulting in this v-shaped graph

rather than a line we had before this

can be transformed in all kinds of ways

that we will learn later for now we just

want to understand some basics about

absolute values what they are and what

they do with that covered let's check

comprehension

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professor Dave explains at gmail.com

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you

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