g is between f and h. fh=8x,fg=6x+7, and gh+28. find fh
To find the value of fh, we need to work with the given equations and use the information provided.
First, let's break down the given information:
1. f is on the left side of g, and h is on the right side of g.
2. fh = 8x, which means the distance between f and h is 8 times some number x.
3. fg = 6x + 7, which means the distance between f and g is 6 times x, plus 7.
4. gh = ?
To find fh, we need to determine the value of x. To do that, we can use the equation fg = 6x + 7 and gh = ?
Since g is between f and h, we know that the distance between f and g added to the distance between g and h should be equal to the total distance between f and h.
Therefore, we can express this relationship as:
fg + gh = fh
Substituting the values we have:
(6x + 7) + gh = 8x
Now, we also know that gh is equal to 28 (given in the problem statement). So, we can substitute gh with 28 in the equation:
(6x + 7) + 28 = 8x
Combine like terms:
6x + 35 = 8x
To isolate x, we need to move the constant term (35) to the other side of the equation:
35 = 8x - 6x
35 = 2x
Now, divide both sides by 2 to solve for x:
35 / 2 = 2x / 2
17.5 = x
We have found the value of x, which is 17.5.
Finally, to find fh, we can substitute the value of x in the given equation:
fh = 8x
fh = 8 * 17.5
fh = 140
Therefore, fh is equal to 140.