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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 a
negative result
it will always produce a 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 x is
equal to seven
what are the possible values of x
x 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
x could be seven or negative seven
both will make the equation true
so now how can we use this to solve a
typical problem
that involves an absolute value symbol
so let's say if we have the function
the absolute value of x 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 x
can be equal to seven
and for the second one
x
is equal to negative eleven
so these are the solutions
find the value of x
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 x 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
x 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 a 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 x minus one
is equal to negative 2.
what's the solution
the absolute value function can never
equal
a negative number
so there's no solution for this
particular example
it can only equal zero or a positive
number
now let's try one more example for this
particular lesson
find the value of x
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 x minus one
is equal to three
and the second x minus one is equal to
negative three
so if we add one
x 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
