12-(2x+1)=1+2x

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labellavita89's profile pic

labellavita89 | High School Teacher | (Level 1) Adjunct Educator

Posted on

12-(2x+1)=1+2x

In this problem we need to solve for x. We want to get the x on one side and the numbers on the other. When solving equations we need to use order of operations. PEMDAS: Parentheses, Exponent, Multiplication/Division, Addition/Subtraction.

Step 1: Parentheses/Distribution

To get rid of the parentheses we need to distribute the negative inside of the parentheses.

                    12-2x-1=1+2x

Step 2: Combine like Terms

We need to combine like terms for any terms that are on the same side of the equation. On the left side of the equation we have 12 and -1 which are like terms.

                   11-2x=1+2x

Step 3: Move the x terms to the left side of the equation (Subtract)

We need to move the 2x that is on the right side to the left side of the equation. The 2x is positive, so to remove it from the right side, we have to subtract it since subtraction is the opposite of addition. We also have to subtract it from the left side because what we do to one side we have to do to the other. It is like a scale, so we have to keep both sides even and do the same thing to both sides. 

                  11-2x-2x=1+2x-2x

                  11-4x=1

Step 4: Move the number not connected to the x to the right side

We need to move the 11 to the right side of the equation. Since 11 is positive, we need to subtract 11 from both sides of the equation.

                  11-4x-11=1-11

                  -4x=-10

Step 5: Move the number connected to the x to the right side

We need to move the -4 to the right side of the equation. Since -4 is being multiplied to x, we need to divide by -4 since division is the opposite of multiplication. 

                  `(-4x)/-4 = (-10)/-4`                   

                   `x= 10/4`

Don't forget that a negative divided by a negative is a positive.

This fraction can be reduced, so the final answer is `x= 5/2`

                   

e-devam's profile pic

e-devam | High School Teacher | (Level 2) Adjunct Educator

Posted on

To solve for x:

`12-(2x+1)=1+2x`

Removing the parenthesis from L.H.S.

` ``12-2x-1=1+2x`

Grouping like terms together:

`-2x-2x=1+1-12`

` ``=gt -4x=-10`

Dividing both sides by -4,

` ``=gt x=10/4=5/2`

Therefore, the value of x is `5/2` .

hardworkingstudent40's profile pic

hardworkingstudent40 | (Level 1) eNoter

Posted on

Ok from there we move the numbers over to the opposite side by adding 11 to each side

-1=-11+4x

+11      +11

Now we can solve!

10=4x

Dovide each side by 4 to get the variable by itself

10/4=

4x/4=x

x=2.5

hardworkingstudent40's profile pic

hardworkingstudent40 | (Level 1) eNoter

Posted on

Here is your equation...

12-(2x+1)=1+2x

Now, let's start with and easy step- subtracting 12 from both sides

12-(2x+1)=1+2x

-12             -12

Here is what we have now

-(2x+1)=-11+2x

Lets put the 'invisible' one in front of the positive side to make things clearer

-1(2x+1)=-11+2x

So now we can use distribution. We need to multiply both the 2x and the +1 by the -1. Now we have...

-2x-1=-11+2x

Now we need to get the like terms to one side. We will start with the variables. Add 2x to both sides.

-2x-1=-11+2x

+2x          +2x

ssandhu05's profile pic

ssandhu05 | Student, Undergraduate | (Level 2) Honors

Posted on

12-(2x+1)=1+2x

To solve this problem, you start with the numbers in the parenthesis. Since there is a negative sign, that means that the value outside of the parenthesis is -1. So you would multiply -1 to the numbers inside the parenthesis.

12-(2x+1)=1+2x

12-2x-1=1+2x

Next, you would start by trying to get "x" by itself.

12-2x-1=1+2x

11-2x=1+2x

10-2x=2x

10=4x

10/4=x

Then you would simplify.

x=5/2 or 2.5

kspcr111's profile picture

kspcr111 | In Training Educator

Posted on

Given

12-(2x+1)=1+2x

let   (2x+1) = (1+2x)=y

so 12-y=y

=> 12=2y

=> y=6

so we can say that 1+2x=6

 => 2x=5
 
 => x=5/2 =2.5

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