Question

1. given: m is the midpoint of \\( \overline { j k } \\)

\\( j m = 5 \\)
prove: \\( m k = 5 \\)

1. given: b is the midpoint of \\( \overline { a c } \\)

\\( a b = 3 x + 6 \\)
\\( b c = - 2 x + 26 \\)
prove: \\( x = 4 \\)

Explanation:

Step1: Use the mid - point property

Since \(B\) is the mid - point of \(\overline{AC}\), by the definition of a mid - point, \(AB = BC\).
So, \(3x + 6=-2x + 26\)

Step2: Solve the equation for \(x\)

Add \(2x\) to both sides of the equation:
\(3x+2x + 6=-2x+2x + 26\)
\(5x+6 = 26\)
Subtract \(6\) from both sides:
\(5x+6 - 6=26 - 6\)
\(5x=20\)
Divide both sides by \(5\):
\(x=\frac{20}{5}=4\)

Answer:

\(x = 4\)