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