Question

what is the value of x?
4x - 8
2x

Explanation:

Step1: Apply the property of congruent right - angled triangles

Since \(MB\) is the perpendicular bisector of \(JK\), \(\triangle MBJ\cong\triangle MBK\) (by the Hypotenuse - Leg congruence criterion for right - angled triangles). So, \(MJ = MK\).

Step2: Set up the equation

We know that \(MJ=4x - 8\) and \(MK = 2x\). Then, \(4x-8=2x\).

Step3: Solve the equation for \(x\)

Subtract \(2x\) from both sides: \(4x-2x - 8=2x-2x\), which gives \(2x-8 = 0\).
Add \(8\) to both sides: \(2x-8 + 8=0 + 8\), so \(2x=8\).
Divide both sides by \(2\): \(x=\frac{8}{2}\).

Answer:

\(x = 4\)