# Variable Expressions

## Key Questions

• Variables are symbols representing some changing quantities.

I hope that this was helpful.

• Variable expressions are expressions that involve variables, which are symbols that represent changing quantities. (See http://socratic.org/questions/what-are-variables for reference). The value of the expression will change as the value of the variable changes.

For example, let's say with have the equation $x + 5$

When $x = 1$, then $x + 5 = 6$

When $x = 2$ then $x + 5 = 7$

• To write variable expressions on Socratic, simply place hash tags around the expression when typing it:

[hash tag] x + 1 [hash tag] = $x + 1$

[hash tag] (x-1)/(x+1) [hash tag] = $\frac{x - 1}{x + 1}$

• To evaluate a variable expression means to find the value of the expression when the variable is (or variables are) replaced by a number (or numbers).

Here is a variable expression: $3 x + 7$.

To evaluate this expression when $x = 2$ mean to substitute $2$ in place of $x$, and find the number (the value). [see note below]

$3 \left(2\right) + 7 = 6 + 7 = 13$.

When $x = 2$, the expression has a value of `$13$.

If we evaluate the same expression when $x = 10$, we get:

$3 \left(10\right) + 7 = 30 + 7 = 37$.

Here's a variable expression with two variables : $3 x - 2 y$

In order to evaluate this expression, we'll need values (numbers) for both $x$ and $y$.

Evaluate the expression $3 x - 2 y$ when $x = 4$ and $y = 5$

$3 \left(4\right) - 2 \left(5\right) = 12 - 10 = 2$

If we change the values to $x = 5$ and $y = 4$, we get
$3 \left(5\right) - 2 \left(4\right) = 15 - 8 = 7$.

Note:

To avoid saying exactly the same thing over and over, we use the following to mean the same thing:

evaluate the expression when $x = 2$
evaluate the expression for $x = 2$
evaluate the expression at $x = 2$
evaluate the expression assuming $x = 2$
evaluate the expression if $x = 2$

Also

If there is only one variable in an expression, we don't always need to mention it:
evaluate the expression for $2$
evaluate the expression at $2$

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