Question

Explain how you get the answer to 7|8-3h|=21h-49

Answer 1

Awnser-H=5/2

Explantion- Absolute value equalitiy entered

     7|-3h+8| = 21h-49  Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is 7|-3h+8|

For the Negative case we'll use -7(-3h+8)  

For the Positive case we'll use 7(-3h+8)  

-7(-3h+8) = 21h-49  

    Multiply

     21h-56 = 21h-49  

    Rearrange and Add up

     0h = 7  

    False, No solution for the Negative Case 7(-3h+8) = 21h-49  

    Multiply

     -21h+56 = 21h-49  

    Rearrange and Add up

     -42h = -105  

    Divide both sides by 42

     -h = -(5/2)  

    Multiply both sides by (-1)

     h = (5/2)  

    Which is the solution for the Positive Case When an absolute value equation has just one solution, that solution has to be checked:

The equality is  7|-3h+8| = 21h-49  

The solution is  h = 5/2  

We check the solution by plugging it for h

7|-3(5/2)+8| = 21(5/2)-49  

The left hand side is equal to   (7/2)  

The right hand side is equal to   (7/2)  

The two sides are equal!

Solution checks!

h=5/2