solotion algebretically

Question

4-x/x-2=-2/x-2

 

volume of a cube V=s3 the length of the cube is round

 

a. 800cm(small) 3

b.500cm(small three)

 

formula for wind chill

 

w=33-(10.45+10Check mark over v-X-V (33-T)/22=

Tis actually Celcius

Answer 1

You know that we can Multiply the Numerator and denominator of a fraction by the same number and the value of the fraction does not change:

 

    1/2 = (2 * 1) / ( 2 * 2) = 3/ 6 = 4/ 8 =  ....... 50/100

 

     This says that if we split a unit, first into 2 part, 2nd into 4 part, 3rd into 6 part, ...... , and into 100 part

 

     1 of the first split, 2 of the 4 split, 3 of the 6 split, ..... , 50 of the 100 split

 

       will all add up the same quantity.

 

      Now:

                   if we have  1/2 = x / 6

 

                    We have 2 fraction equal, therefore, 6 divided by 2 = 3 , X has to be multiplied by 3 to keep                     the values of 2 fractions equal

                     to solve this equation:

                       1/2 = x/6

 

                       We multiply both sides by 6

 

                        6*1/2  = 6 *X / 6

                           

                        Now divide both sides by 6

 

                          Simplify each fraction

                           

                             X = 3

                So , that is where the cross multiplication of 2 equal fraction comes into picture.

                  Multiply both fraction with LCM of the denominators, and then simplify each fraction to find the

                   value of the variable.  

 

 

Answer 2

Hello again Sherry -

The first equation above is called an algebraic rational expression. This is just a fraction with variables in it. Look at the equation. If there were no x's in it, what would you do? Isn't it just a proportion? It is two fractions set equal to each other. I would start solving this by cross multiplying. Then you get the following: 

 

-2(x-2) = (4-x)(x-2) 

 

Now distribute the negative 2 on the left and FOIL the right side, combine like terms and get this: 

 

x² -8x +12 = 0

 

Now can you factor the quadratic? When I do this I get

 

(x-6)(x-2) 

 

Now use the Zero Product property, set each factor equal to zero and solve. You get two answers, 6 and 2. BUT..... you need to check you answers. What happens in the denominator of the original equation if x = 2? Uh-oh! the denominator would be equal to zero, so 2 is called an "excluded value", and the only valid solution is 6. 

 

Let's check; 4-6/6-2 = -2(6-2)? 

-2/4 = -2(4) 

Voila! it checks!