3x+2 = 4(x-1)-1

Question

Not sure if the steps I am following are correct? I have an answe, but get confused with how we work with the fraction and variable or cross multiplying.

Answer 1

3x+2=4x-4-1
3x +2=4x -5
4x -5 =3x +2
4x -3x = 2+5
x=7

Answer 2

I can see how this equation can get confusing.  One way to lessen the confusion is to "chunk" the equation into smaller, mini equations so that it is less taxing on the mind and eyes.  Using the algebraic equation you provided, I will show you what this looks like.

1.  3x+2 = 4(x-1)-1   : Work one side of the equation at a time until you have no choice but to work with both sides.  In this case, the left side of the equation is at a point where there is nothing to do at this time, so ignore that side for now and put all your attention into the right side.

2. 4(x-1)-1  : One item at a time, you should multiply 4 be each item in the parentheses.  so when you're done doing that, the right side of the equation should like like :  (4x -4)-1  . 

3. You can get rid of the parentheses so it looks like: 4x-4-1. 

4. There's a little left you can do before you work with both the left and right sides of the equation. -4-1 is -5. So now on the right side you are left with 4x-5.  There is nothing you can do further unless you bring in the left side of the equation.

5.  Now we are working with 3x+2=4x-5.   At this point, always remember that what you do with one side, you must do with the other.

6. From here, subtract 2 from both sides so that you can work towards getting 'x' by itself, thus solving for x.    It should look like this, 3x+2-2=4x-5-2 .  The twos on the right side cancel each other out because they are a negative and positive equal number.  And the -5-2 can be added on the left side.

7.  Now the equation will look like this, 3x=4x-7.  If you subtract 4x from each side then all the x's will be on one side. It should look like this, 3x-4x=4x-4x-7.  Again, the 4x and -4x will cancel each other out and now we can solve 3x-4x, which is -1x or -x. 

8. The equation should look like this, -1x=-7.  Now we can divide each side by -1 to get x by itself and as a positive.  So the equation will look like, -1x/-1=-7/-1

9. Finally, the equation should look like, x=7. And now we can check our answer of 7 by replacing all the x's with 7 and solving the equation.

 

Hope I've broken it down well enough for you.  Best of Luck to you!

Answer 3

Sesha,

Generally, you want to (1) distribute across the parentheses and then (2) add/subtract to put all the x's on one side and everything else on the other.  If what I've written does not make sense, feel free to email me, I'd be happy to follow-up.

Step 1.  Here, you need to distribute the 4 over the parentheses on the right hand side.  So you will have how many x's and subtract how much?

Step 2.  In this case, I would recommend bringing all the x's to the right hand side and all the other numbers to the left hand side, while keeping the equation balanced, so something like this:

3x + 2         = 4x - 4 - 1

-3x + 4 + 1  = -3x + 4 + 1
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[3x-3x=0x  |  4x-3x =x

2+4+1=7   | -4-1+4+1=0]

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7               =  x