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### Course: Algebra basics>Unit 2

Lesson 1: Introduction to variables

# Evaluating expressions with one variable

A mixture of explanations, examples, and practice problems to have you evaluating expressions with one variable in no time!

## How to evaluate an expression with one variable

Let's say we want to evaluate the expression $a+4$. Well, first we need to know the value of the variable $a$. For example, to evaluate the expression when $a=1$, we just replace $a$ with $1$:
So, the expression $a+4$ equals $5$ when $a=1$.
We can just as easily evaluate $a+4$ when $a=5$:
So, the expression $a+4$ equals $9$ when $a=5$.

## Evaluating an expression with multiplication

You might be asked to "Evaluate $3x$ when $x=5$."
Notice how the number $3$ is right next to the variable $x$ in the expression $3x$. This means "$3$ times $x$". The reason we do this is because the old way of showing multiplication with the symbol $×$ looks confusingly similar to the variable $x$.
Okay, so now let's solve the problem:
So, the expression $3x$ equals $15$ when $x=5$.

### New ways to show multiplication

Hold on a second! Did you notice that we wrote "$3$ times $5$" as $3\cdot 5$ instead of as $3×5$? Using a dot instead of the symbol $×$ is another new way of showing multiplication:
$3\cdot 5=15$
Parentheses can also be used to show multiplication:
$3\left(5\right)=15$
Let's summarize the new ways of showing multiplication that we learned.
Old wayNew way
With a variable$3×x$$3x$
Without variable$3×5$$3\cdot 5$ or $3\left(5\right)$

## Evaluating expressions where order of operations matter

For more complex expressions, we'll have to be sure to pay close attention to order of operations. Let's take a look at an example:
Evaluate $5+3e$ when $e=4$.
So, the expression $5+3e$ equals $17$ when $e=4$.
Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is $32$, which comes from first adding $5$ and $3$ to get $8$ then multiplying $8$ by $4$ to get $32$.

## Let's practice!

Problem 1
Evaluate the expression $9-z$ when $z=4$.

## Challenge problems

Challenge problem 1
Evaluate $e\cdot e-5e$ when $e=5$.

## Want to join the conversation?

• I still don't understand the challenge problems e⋅e−5ee, dot, e, minus, 5, e when e=5e=5e, equals, 5.What does this mean?
• so, e(dot)e - 5e, the dot symbol represents multiplication. And 5e is another way to represent multiplication so, the expression actually looks like this: 5x5 - 5x5 which equals to 0 because 5x5 = 25, and 5x5 = 25, and subtracting 25 with 25 = 0.

e(dot)e - 5e
5x5 - 5x5 = 25 - 25
25 - 25 = 0
• If 9-8/x = ? and x=4 what do I do with the 8/x? Do I multiply add divide or subtract?
• you substitute for x, so 9 - 8/4, do divide (8/4) first then subtract from 9.
• Why do we have to do multiplication and division first? Why to use these "order of operation"?
• Here is why; "Because exponents are simply repeated multiplication, they are performed before multiplication. ... Thus the order: parentheses first, exponents second, mutiplication and division third, and save the lowest level operations of addition and subtraction for last." Personally I believe order of operation is way to balance the equation as well. :)
• If you don't know what y is, then you won't get an exact answer
• Well you don't need to know what y is to solve the question. For example you have:6t=48. (if something is written like 6t, that always means you have to multiply, or any variable). So we have: 6t=48, we can divide both sides by 6 (we are dividing because you always do the inverse of what you are trying to solve, the opposite of multiplication is division)

we have to divide both sides by 6

6t=48, 6/6 cancels out, 48/6=8. So now the equation would look like this: t=8, and now we know what t is we can verify it. 6t=48 or 6x8=48.

And that's the beauty of Algebra!

If you need more help just tell me.
-Intellectual Genius
• what is it asking me when it says Evaluate 2y2y when y = 6y=6
• It means you use substitution... You replace the "y" in "2y" with the value you are given. Since you were told to use "y=6", you take out "y" and replace it with 6. Remember, "2y" means "2 times y", so you need a multiplication symbol. Thus, "2y" becomes "2(6)".
Then, you simplify the expression by doing the multiplication. Your final answer would be 12.

Hope this helps.
• is it just me or is it way easier here than in class?
• way easier
• Start out with the variable. What is d worth? What do you need to do with that variable in the sentence? You should see that d is worth 4, and we need to now add that in the sentence.

The sentence should now look like this -
8/4 + 3

Now, solve it like you would usually do it. 8/4 is equal to 2 (We need to do it first since it is the second in the Order of Operations), and then add 3 to that 2. You should get an answer of 5 if you did all that calculation correctly.

Hope this helped!