Answer
$x = 11$
Work Step by Step
From the diagram, we have a line segment that joins the midpoint of two sides of a triangle. According to the triangle midsegment theorem, if a line segment joins two sides of a triangle at their midpoints, then that line segment is parallel to the third side of that triangle and is half as long as that third side.
Knowing this information, we can deduce that this line segment is half of the length of the third side to which it is parallel. Let's set up that equation accordingly:
$3x - 1 = 2(x + 5)$
Use the distributive property first:
$3x - 1 = 2x + 10$
Add $1$ to each side of the equation to isolate constants on one side of the equation and the variable on the other:
$3x = 2x + 11$
Subtract $2x$ from each side of the equation to isolate the variable on the left side of the equation:
$x = 11$
