Soving 8th grade equations

[pinkiethepig]

Somebody help me solve this equation (show me all steps!!): 4x-9=3-4x, I got that you have to subtract one of the 4x from the other but I don't understand how to do the rest and if there is anything that comes before the step before 4x-4x than please tell me. Thanks for reading this and I jope that you reply. Show proof please.

 

[jwpaine]

Somebody help me solve this equation (show me all steps!!): 4x-9=3-4x, I got that you have to subtract one of the 4x from the other but I don't understand how to do the rest and if there is anything that comes before the step before 4x-4x than please tell me. Thanks for reading this and I jope that you reply. Show proof please.

\(\displaystyle 4x-9=3-4x\)

Isolate x on one side

\(\displaystyle 4x-9 + 4x=3-4x + 4x\)
\(\displaystyle 8x-9=3\)

...you continue

John.

 

[nycfunction]

Somebody help me solve this equation (show me all steps!!): 4x-9=3-4x, I got that you have to subtract one of the 4x from the other but I don't understand how to do the rest and if there is anything that comes before the step before 4x-4x than please tell me. Thanks for reading this and I jope that you reply. Show proof please.

We have this linear equation:

4x - 9 = 3 - 4x....This is read: "Four times x minus nine equals three minus four times x."

We need to solve for x. Solving for a variable (a letter) means to find the value of the letter we are asked to solve for. Got it?

Keep in mind that crossing the EQUAL sign changes the sign IN FRONT of the number, term or variable.

Is this clear?

Let's combine LIKE TERMS.

In other words, re-arrange the equation.

4x + 4x = 3 + 9...Do you see that -4x on the right side of the equation became positive 4x when it crossed over to the left side?

Do you also see that 9 became positive 9 when it crossed over to the right side?

We now have this:

8x = 12

We divide BOTH sides of the equation by 8 to find the value of x. By the way, the number 8 is called a COEFFICIENT. A coefficient is simply a number "standing" next to a letter.

Got it?

THEN:

x = 12 divided by 8

x = 12/8

The fraction 12/8 can be reduced to the lowest term.

What is the BIGGEST number that 12 and 8 can be divided by WITHOUT a remainder?

How about 4?

12 divided by 4 = 3.

8 divided by 4 = 2.

We have a new, REDUCED fraction and it is 3/2.

So, x = 3/2

Final answer: x = 3/2

Can we prove that x = 3/2?

Sure we can.

We REPLACE x with the fraction 3/2 in the ORIGINAL equation given. If we get the same answer on BOTH sides if the equation, we will know that x = 3/2 is the right answer.

Let's try it.

You were given:

4x - 9 =3 - 4x

x = 3/2, right?

Everywhere you see x, replace it with the fraction 3/2 and simplify.

Simplify means: DO THE MATH!!

4(3/2) - 9 = 3 - 4(3/2)

6 - 9 = 3 - 6

-3 = -3...IT CHECKS!!! We got the same answer on BOTH sides of the equation proving that the right answer is x = 3/2.

Is this clear?

 

[Loren]

I don't mean to disagree with the other explanations offered. Because, there may still be confusion, I offer this....

The basic concepts in solving an equation in one variable is to do the same thing to both sides of the equation, selecting what to do, so that you finally end up with "one" variable on one side and a single number on the other side.

4x - 9 = 3 - 4x
We are trying to get 1x on one side of the equation, so, we must get rid of one of the "4x's". If you choose to eliminate the -4x from the right side of the equation, you will add +4x to both sides. If you choose to eliminate the +4x from the left side, you will subtract 4x (or add -4x) from both sides. Let's do the former.

4x - 9 + 4x = 3 - 4x + 4x.

Now, simplify that.

8x - 9 = 3

Now, we need to get rid of the -9 from the left side. We do so by adding 9 to both sides.

8x - 9 + 9 = 3 + 9

Now, simplify.

8x = 12

We now know the value of 8 of those x's, but we want to know the value of only one of them. Therefore, if we have eight of them, to get one of them we will divide by 8. If we divide the left side by 8 we must divide the right side by 8. (We have made the left side one-eighth as large as it was, so, to maintain the equality, we must make the right side one-eighth as large as it was.)

\(\displaystyle \frac{8x}{8}=\frac{12}{8}\)

Simplify and reduce if possible.

\(\displaystyle x=\frac{12}{8}=\frac{3}{2}\)

I leave the check to you as explained above.