Point H is on line segment \overline{GI}
GI
. Given GH=x+6,GH=x+6, HI=x+5,HI=x+5, and GI=3x+8,GI=3x+8, determine the numerical length of \overline{GH}.
GH
.
We are given that GH = x + 6, HI = x + 5, and GI = 3x + 8. To find the length of GH, we need to find the value of x and substitute it into GH = x + 6.
Since H is on line segment GI, the sum of GH and HI should be equal to the length of GI. We can write this as an equation:
GH + HI = GI
Substituting the given values, we have (x + 6) + (x + 5) = 3x + 8.
Simplifying the equation, we get 2x + 11 = 3x + 8.
Subtracting 2x from both sides, we have 11 = x + 8.
Subtracting 8 from both sides, we get 3 = x.
Now, substitute the value of x into GH = x + 6.
GH = 3 + 6
GH = 9.
Therefore, the numerical length of \overline{GH} is 9.
To find the length of line segment GH (denoted as |GH|), we need to determine the numerical value of x in the given equation GH = x + 6.
First, we know that GH + HI = GI according to the segment addition postulate. Substituting the given values, we have:
x + 6 + (x + 5) = 3x + 8.
Simplifying the equation, we combine like terms:
2x + 11 = 3x + 8.
To isolate the x term on the right side of the equation, we can subtract 2x from both sides:
2x - 2x + 11 = 3x - 2x + 8,
which simplifies to:
11 = x + 8.
To solve for x, we can subtract 8 from both sides:
11 - 8 = x + 8 - 8,
which simplifies to:
3 = x.
Therefore, the numerical length of line segment GH is |GH| = x + 6 = 3 + 6 = 9.
So, |GH| = 9.
Just say "segment GI" all the formatting junk is just annoying. Especially the part where you repeat it needlessly.
Now. Draw the line segment and label the various data as give. Note that
GI = GH+HI
3x+8 = x+6 + x+5
x = 3
Now you can answer the question.