I am always confused to how to find x in algebra??

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sciftw's profile pic

sciftw | High School Teacher | (Level 1) Educator Emeritus

Posted on

I completely understand.  I always thought math got a bit goofy once I started seeing more letters than numbers.  Finding a single unknown (x) can be tricky at times, but finding a single unknown is a lot better than finding multiple.  

Your tactic is to isolate x on one side of the equals sign.  If it starts already isolated, you are done.  Something like  x = 5.  That's very straight forward, but at times the x can be more.  For example x = 20/5.  If that's the case, then simplify the one side.  x = 4.  X could also involve other unknowns: x = 5y.  If that's the case, you could be done.  If you know what the value of y is, then apply the y value and solve for x.  

In most cases involving x, you will need to work the problem to isolate x as the above examples do.  Let's give a specific example.  Distance = Speed x Time.  If a car drove 480 miles in one day, and it only ever drove 60 mph hour, how long did the drive take? Set up your equation with your known values 480 = 60(x).  You do not have x alone on one side of the equals sign.  Your job is to do that. In order to do that with my example, you need to divide both sides by 60.  You do that because x is being multiplied by 60.  You have to "undo" that.  But you must do it to BOTH sides of the equation.  

480/60 = (60x)/60

Dividing the right side by 60 causes the value to cancel out and leave you with just x.  

8 = x.  So the drive took 8 hours.  

You could have more advanced equations with x.  Remember your order of operations (PEMDAS) and work backward.  

500 = 10x + 50  

Subtract 50 from both sides

450 = 10x

Divide both sides by 10

45 = x

I'm sure you are looking at much more difficult equations, but the method doesn't change to isolate x.  

lisachoate's profile pic

lisachoate | eNotes Newbie

Posted on

Remember that in algebra we use letters to represent unknown values. The trick is to "undo" to equation to find x.

For example: 3+x=9

Since we need to know x, we want to get x by itself.  We want the equation to look like x=some number.

To get x by itself, we need to move everything that is on the same side as x. In our example, 3+x=9, we need to move the 3. To "undo" the equation, we just do the opposite. To move 3 over, we take it over to the right and do the opposite.  The opposite of 3 is -3. The equation becomes:

x=9-3

x = 6.  Now let's be sure 6 is correct by substituting it for x and see if we get a true statement.

3+x=9

3+6=9

9=9 YES!

Another example:

7=x-5

7+5=x

12 = x

And another:

5x = -15

x= -15/5 (since the opposite of multiplying by 5 is dividing by 5)

x = -3

Hope this helped!

studylover's profile pic

studylover | eNotes Newbie

Posted on

you need to learn algebraic expressions. 

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