Point M is the Midpoint of Segment QR. If QM = 2x + 5 and MR = 5x – 1, Find the Length of QR.

To find the length of segment QR, we start by using the fact that point M is the midpoint. This means that QM is equal to MR:

QM = MR

Substituting the expressions given:

2x + 5 = 5x – 1

Now, we will solve for x:

1. First, we will move the terms involving x to one side and the constant terms to the other side:

2x – 5x = -1 – 5

2. Combining like terms gives us:

-3x = -6

3. Now, divide both sides by -3:

x = 2

Now that we know x, we can find the lengths of QM and MR:

• QM = 2(2) + 5 = 4 + 5 = 9
• MR = 5(2) – 1 = 10 – 1 = 9

Since QM and MR are both equal and measure 9 units, we can now find the length of QR:

QR = QM + MR = 9 + 9 = 18

Thus, the length of segment QR is 18 units.