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## Algebra (all content)

# 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, plus, 4. Well, first we need to know the value of the variable a. For example, to evaluate the expression when start color #11accd, a, equals, 1, end color #11accd, we just replace start color #11accd, a, end color #11accd with start color #11accd, 1, end color #11accd:

So, the expression a, plus, 4 equals 5 when a, equals, 1.

We can just as easily evaluate a, plus, 4 when start color #11accd, a, equals, 5, end color #11accd:

So, the expression a, plus, 4 equals 9 when a, equals, 5.

## Evaluating an expression with multiplication

You might be asked to "

**Evaluate 3, x when x, equals, 5.**"Notice how the number 3 is right next to the variable x in the expression 3, x. This means "3 times x". The reason we do this is because the old way of showing multiplication with the symbol times looks confusingly similar to the variable x.

Okay, so now let's solve the problem:

So, the expression 3, x equals 15 when x, equals, 5.

### New ways to show multiplication

Hold on a second! Did you notice that we wrote "3 times start color #11accd, 5, end color #11accd" as 3, dot, start color #11accd, 5, end color #11accd instead of as 3, times, start color #11accd, 5, end color #11accd? Using a dot instead of the symbol times is another new way of showing multiplication:

Parentheses can also be used to show multiplication:

Let's summarize the new ways of showing multiplication that we learned.

Old way | New way | |
---|---|---|

With a variable | 3, times, x | 3, x |

Without variable | 3, times, 5 | 3, dot, 5 or 3, left parenthesis, 5, right parenthesis |

## 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, plus, 3, e when start color #11accd, e, equals, 4, end color #11accd.**

So, the expression 5, plus, 3, e equals 17 when e, equals, 4.

Notice how we had to be careful to think about order of operations when evaluating. A common wrong answer is start color #e84d39, 32, end color #e84d39, which comes from first adding 5 and 3 to get 8 then multiplying 8 by 4 to get start color #e84d39, 32, end color #e84d39.

## Let's practice!

## Challenge problems

## 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?(38 votes)
- 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(63 votes)

- If 9-8/x = ? and x=4 what do I do with the 8/x? Do I multiply add divide or subtract?(25 votes)
- you substitute for x, so 9 - 8/4, do divide (8/4) first then subtract from 9.(26 votes)

- If you don't know what y is, then you won't get an exact answer(9 votes)
- 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(19 votes)

- Why do we have to do multiplication and division first? Why to use these "order of operation"?(2 votes)
- 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. :)(19 votes)

- so u saying if i put 5 + 2b and be equal to 5 the answer would be 15(8 votes)
- what is it asking me when it says Evaluate 2y2y when y = 6y=6(8 votes)
- 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.(1 vote)

- this is so easy im in Geometry(4 votes)
- what does 2(3) mean?

(4th question in practice)(5 votes)- It is 2 times 3 which is 6(5 votes)

- i can't understand the question nine please help me understand(5 votes)
- 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!(4 votes)

- im still having trouble with this math(3 votes)
- We are trying to evaluate an expression for a given value. So lets say that you can buy a bottle of coke for 1.50. If you buy 1 bottle, you pay 1.50, two bottles cost 3 dollars, 3 bottles is 4.50, 4 bottles cost 6 dollars, and so on. The store does not care how many bottles you buy, but they may only have 100 bottles, so you could not buy more than what they have. So we could create an expression of 1.50x for this situation. Then for any number up to 100 bottles we could calculate the cost by substituting the number of bottles in for x. Lets say you want to buy 4 bottles (which means x=4), you would have 1.50 (4) =6 dollars which is what we would expect. What if you want 22 bottles? Do you want to keep adding 1.50 a bunch of times, or use the expression 1.50(22) to find the answer?

One thing I recommend to my students is to just put the substituted number in () whenever you see the variable. If you have x^2 + 3x - 4, we can evaluate it for any value, so I will make up 3 values, -4, 0, and 4. Every time I see an x, lets put the number in parentheses. For -4, we get (-4)^2+3(-4)-4. For 0 we get (0)^2+3(0)-4, and for 4 we get (4)^2+3(4)-4. By putting in parentheses, it should take care of any sign issues.(2 votes)