The value of x in the expression for the measure of the segments of the triangle is 4.
The figure in the image is a triangle with a segment DE joining the midpoints of two of its sides.
To determine the values of x, we use the mid-segment theorem which is expressed mathematically as:
Smaller segment = half the third side
From the figure;
The smaller segment = DE = ( x + 1 )
The larger segment = BC = ( 4x - 6 )
Plug the given values into the above formula and solve for x:
DE = 1/2 × BC
( x + 1 ) = 1/2 × ( 4x - 6 )
2( x + 1 ) = 2 × 1/2 × ( 4x - 6 )
2( x + 1 ) = ( 4x - 6 )
2x + 2 = 4x - 6
4x - 2x = 2 + 6
2x = 8
x = 8/2
x = 4
Therefore, the numerical value of x is 4.