Q is the midpoint of PR. PQ = 3x - 5 and QR = x + 17. What is the value of x?
3x-5=x+17
To find the value of x, we can use the fact that Q is the midpoint of PR.
According to the midpoint formula, the coordinates of the midpoint (Q) of a line segment with endpoints (P) and (R) are the average of the coordinates of P and R.
In this case, Q is the midpoint of PR, so we can set up the following equation:
PQ + QR = 2(QP)
Substituting the given values:
(3x - 5) + (x + 17) = 2(x + 17 - 3x + 5)
Simplifying the equation:
4x + 12 = 2(x - 3x + 22)
4x + 12 = 2(-2x + 22)
4x + 12 = -4x + 44
Combining like terms:
8x + 12 = 44
Subtracting 12 from both sides:
8x = 32
Dividing by 8:
x = 4
Therefore, the value of x is 4.
To find the value of x, we need to use the fact that Q is the midpoint of PR.
In a line segment, the midpoint divides the segment into two equal parts. So, we can set up an equation using the given lengths of PQ and QR.
Since Q is the midpoint of PR, we can say that PQ = QR. Therefore, we have the equation:
3x - 5 = x + 17
To solve for x, we will isolate the x term on one side of the equation:
3x - x = 17 + 5
Simplifying the equation:
2x = 22
Finally, to solve for x, we divide both sides of the equation by 2:
2x/2 = 22/2
x = 11
So, the value of x is 11.