We’ll use the segment addition postulate, which states that we can add two adjacent (next to each other) segments to find the total length.
We are given the total length as segment GI=2x+15, and we will solve for x. So, we can add the two expressions together to equal the length of segment GI.
Let’s form an equation:
GH+HI=GI
Substitute the corresponding values in for GH, HI, and GI:
(3x+8)+(2x+1)=2x+15
Solve for x:
Combine like terms:
(3x+2x)+(8+1)=2x+15
5x+9=2x+15
Subtract 2x from both sides:
5x-2x+9=15
3x+9=15
Subtract 9 from both sides:
3x=15-9
3x=6
Divide both sides by 3:
3x/3=6/3
x=2
Let’s check if this is correct. Substitute x=2 back into the equation:
(3(2)+8)+(2(2)+1)=2(2)+15
Simplify using PEMDAS:
(6+8)+(4+1)=4+15
14+5=4+15
19=19
So, the answer is: x=2