hey it's kayleigh in this lesson we're going to use what we know about algebraic expressions to
evaluate some expressions with a variable we're really doing algebra now let's go
let's start with an example here we have an expression that says three x plus four and we
need to evaluate it when x is equal to 2. now what does 3 x mean yeah that's right it means 3 times x
it is a product and what do we call x yeah a variable that's right so that makes 3 a constant
times a variable and what do we call that a coefficient great work so this problem is telling
me that my variable x is equal to 2. so i'm going to use a strategy called substitution substitution
just means we're going to replace one thing with another in the case of expressions with one
variable we're going to replace the variable with the given value i'm going to write my expression
3x plus 4 and wherever i see my variable x i'm going to substitute a 2.
notice that i put parentheses about around my substitution what do these parentheses mean
that's right they mean multiplication this helps me know that i mean 3 times 2 and not the number
32 great now we can evaluate our expression using order of operations first we multiply
three times two is six and then we add the four and we know six plus four is ten so this means
when this expression is evaluated when x is equal to 2 we get an answer of 10.
with this next example i'm going to show you three simple steps that will help us evaluate
expressions with one variable step one is easy we write the expression in our own handwriting
step two wherever we see the variable we use substitution and plug in our given value
and step three we evaluate our expression using order of operations so let's give it a try
so starting with step one i write the expression in my own handwriting so it is m plus 3m minus 10.
okay step two wherever we see the variable we use substitution and plug in our given value so in my
expression where do i have variables yeah i have two of them right in my first term i have an m
and in my second term i have three times my variable m now i need to plug in the given value
where is my given value yeah it's up here where it says m equals four so wherever i see my variable
i'm going to plug in my given value of four so it's going to look like this m becomes a four
plus 3 times 4. remember i'm using my parentheses here because this means 3 times 4 and not just
the number 34. that's not right and then i end my expression with minus 10. perfect so i have all
numbers in here so i can go to step 3 and evaluate my expression using the order of operations so
that would mean i do my multiplication first so i have 4 plus 3 times 4 which is 12 minus 10
and i'm going to combine my addition here 4 plus 12 that would give me 16 minus 10 and 16 minus 10
that's right it's 6. so this is the answer to my expression when i evaluate it for a given
value m equals four amazing chloe is a track star her favorite race to run is the 200 meter dash
that means she runs a distance of 200 meters we can call that distance d
chloe's fastest time running the 200 meter dash is 25 seconds let's call her fastest time
t1 her slowest time running the 200 meter dash is 29 seconds let's call her slowest time
t2 chloe wants to know what her speeds were for each of these races the equation for speed is
distance divided by time and we can simplify that and write it as s equals d over t now if chloe
always runs the 200 meter dash we know that the d is a constant so we can write it as s equals 200
meters over t but there is a variable we know that the time it takes chloe to run 200 yards can vary
so let's rewrite this equation when t is equal to t1 so we'd have s is equal to 200 meters
divided by t1 her fastest time so let's plug in t1 we'd have her speed is equal to 200 meters divided
by we're substituting t1 is that given value up here 25 seconds so we know this is 25 seconds and
now that we've done our substitution we can evaluate using order of operations which in this
case is just division so 200 divided by 25 that would give us 8. so that means chloe's speed was 8
meters per second when she was running her fastest race now we need want to also know her speed
when she ran 200 meters at her slowest time t 2 and we have the given value for t2 here 29 seconds
so we can substitute we have 200 meters divided by t2 substituting 29 seconds and now we can evaluate
you might need a calculator for this one it's 6.8
meters per second was chloe's speed when she ran her slowest time so we can see that chloe
was running at a faster speed 8 meters per second is faster than 6.89 meters per second
when she was running her fastest race and that makes sense so here we use those same three
steps to evaluate an expression with one variable t when t was 25 seconds and when t was 29 seconds
great work now you're ready to practice evaluating expressions with one variable
on your own you can use those three simple steps to help you out have fun and remember to always be
clever