Solve with Given Values

When you first look at it, algebra looks like math with letters.

But, what you quickly learn is that those letters, called variables, represent numbers.  You just don't know what numbers they represent yet!

In advanced algebra problems, you will solve for these variables (or the lines created by these variables).

But, at the most basic level, you can always replace variables in equations with the numbers that those variables stand for. 

Some algebra problems simply want to test whether or not you know how variables work, and just ask you to plug in values for variables.  When you come across a problem like this, you just need to replace the variable with the value provided (in algebra, we call this substitution), and solve.

Example:

If $x=13$ what is the value of $x+12$?

You know that:

$x=13$

So, you will simply take the equation and substitute (13) for every $x$ in the given equation.  Then use math to solve:

$$\eqalign{x+12&=\\(13)+12&=\\&=25}$$

Some equations are a little more complicated, but the subsitution process remains the same:

Example:

If $g=3$ what is the value of $4g+3g$?

You know that:

$g=3$

So, you will simply take the equation and substitute (3) for every $g$ in the given equation.  Then use math to solve:

$$\eqalign{4g+3g&=\\4(3)+3(3)&=\\12+9&=21}$$

Have you noticed that we always subtitute our value in parentheses?  There's a reason for that.  When you substitute, you don't want to lose negative signs, either in the plug in value or in the equation.  Using parentheses helps prevent you from dropping negative signs!:

Example:

If $p=5$ what is the value of $8p-p$?

You know that:

$p=5$

So, you will simply take the equation and substitute (5) for every $p$ in the given equation.  Then use math to solve:

$$\eqalign{8p-p&=\\8(5)-(5)&=\\40-5&=35}$$

Notice how using the parentheses prevented us from losing the minus sign?  Parentheses are even more useful when the value you're substituting has a negative sign.

Example:

If $y=-4$ what is the value of $4y - y$?

You know that:

$y=-4$

So, you will simply take the equation and substitute (-4) for every $y$ in the given equation.  Then use math to solve:

$$\eqalign{4y-y&=\\4(^-4)-(^-4)&=\\^-16- ^-4&=-12}$$

You can see, when there are a lot of negative signs, parentheses help keep them straight!

As equations get more complicated, you might have several variables, but you can plug in values for whatever variables you're given values for.  And then, you can either solve the equation, or solve for a remaining variable.

Example:

If $\dfrac{ab}{4}+c=12$, $a=3$ and $b=8$ what is the value of $c$?

You know that:

$a=3$

$b=8$

So, you will simply take the equation and substitute (3) for every $a$  and (8) for every $b$ in the given equation.  Then use algebra to solve for $c$:

$$\eqalign{\dfrac{ab}{4}+c&=12\\\dfrac{(3)(8)}{4}+c&=12\\\dfrac{24}{4}+c&=12\\6+c&=12\\-6 \; & \; -6\\c&=6}$$

Just plug in and solve!  

Just remember that every variable represents a number.  If you are given the number that the variable represents, subsitute the value for the variable, and then do the math!