1/2x=12 ???

Question

i dont understand how to do the fractions for the equations

Answer 1

Hi, Grace.

You already know that you have to "undo" what is done to the x. You would divide by 1/2 to solve this. Remember, though, that to divide by a fraction, you actually multiply by the reciprocal of the fraction. So to solve this, you multiply both sides of the equation by the reciprocal of the fraction. 1/2 --> 2/1

(2/1) 1/2x = 12 (2/1)

1x = 24/1  

x = 24

To check, substitute 24 back into the equation:

1/2 (24) = 12

It works!

Hope this helps.

Answer 2

The problem is to solve for x when 1/2x=12.

First, think about how 1/2x could be rewritten:

       1/2x = (1/2)(x/1) = x/2

So, in this problem, x/2 =12.

Now, multiply each side by 2.

The result is x=24.

Answer 3

To solve an equation, there are a couple of key concepts.

1. To simplify equations with fractions, you want to attempt to eliminate the fraction by multiplying it by it's reciprocal to get a whole number.

2. To solve for a variable such as x, you perform the inverse operation of the variable. 

3. Whatever operation is performed on one side of the equation, the identical operation must be performed on the other side.

To apply the above concepts to this equation

1/2x=12

1. Eliminate the fraction by multiplying both sides by the reciprocal of 1/2 which is 2.

2(1/2)x = 12(2)  

In this equation   x= 24

In this equation, eliminating the fraction also solved the equation.

___________________________________________________________________

Let's do another example to demonstrate all 3 concepts.

1/2x + 3x  =  21

Step 1. Eliminate the fraction by multiplying each term on both sides by the reciprocal of 1/2 which is 2.

(2)1/2x +  (2)3x= 2(21)

= x+6x = 42

Combine like terms to simplify the equation  ( x + 6x = 7x)

Therefore 7x=42

Perform the inverse operation of 7x (multiplication) with division. You would divide both sides by 7

7x/7 = 42/7

x = 6

Always check your answer by substituting it into the original equation.

1/2x + 3x = 21 ( substitute 6 for x)

1/2 (6) + 3(6) = 21

3 + 18 = 21

21 = 21