We want to evaluate the following expressions
for the given values,
and then use the graphing calculator to check the answer.
We first have the expression five x minus eight
We want to evaluate this for x equals negative nine,
and since five x means five times x,
when we substitute negative nine for x,
we would have five times negative nine minus eight.
Now to evaluate this, we follow the order of operations,
so we multiple before we subtract,
and since five times negative nine equals negative 45,
we have negative 45 minus eight,
which is equal to negative 53.
Let's go ahead and check this.
We have five times negative nine
minus eight, which does equal negative 53.
Next we have the expression two minus four x.
We want to evaluate this when x equals negative seven,
so we substitute negative seven for x.
Remember four x means four times x,
so we have two minus four times negative seven.
Following the order of operations,
we do multiply before subtracting,
so we would have two minus four times negative seven
equals negative 28.
And here we have minus negative 28,
which is equivalent to just plus 28,
so we have a sum of 30.
Now in this example, I do want to point out
that we could've skipped this step here.
We can think of this as negative four times negative seven,
which is equal to positive 28, giving us plus 28,
as we see here.
Either way, the result is 30.
And checking this on the calculator,
we have two minus four times negative seven,
which is equal to 30.
Next we have one-half bh for b equals four
and h equals equals 9.5.
Notice how we have a fraction here and decimal for h.
We normally don't want to mix fractions and decimals,
so let's convert 9.5 to an improper fraction.
Well 9.5 is equal to a nine-and-a-half.
Converting this to an improper fraction,
the denominator would be two,
the numerator would be two times nine plus one,
which would be 18 plus one, or 19.
So instead of using 9.5 for h,
we'll go ahead and use 19-halves.
So now performing the substitution,
we'd have one-half times b, which is four.
Because we have a fraction here,
let's write four over one,
times h, which we'll write as 19-halves,
and now before we multiply, we'll simplify.
Notice two and four share a common factor of two.
There's one two in two and two twos in four.
And notice out here we have a common factor of two as well.
There's one two in two and one two in two.
So simplifying, notice how we're just left
with one times one times 19, which is 19,
all over one times one times one, which is one.
So this simplifies nicely to 19.
Let's go ahead and check this on the calculator.
On the calculator we can just use 9.5.
So we have one-half
times four times 9.5
and Enter, verifying our answer.
Next we have five x squared plus six x minus three.
We want to evaluate this when x equals two,
so we substitute two for x.
So we'd have five times two squared
plus six times two minus three.
Following the order of operations,
we first want to simplify the exponent here.
Two squared is equal to four,
so we'd have five times four plus six times two minus three.
Next we multiply.
Five times four is equal to 20.
Six times two is equal to 12.
And now we add add and subtract from left to right.
20 plus 12 is equal to 32.
32 minus three is equal to 29.
Let's check on the calculator.
Five times two squared
plus six times two
and minus three.
Once again, verifying our answer is correct.
I hope you found this helpful.