Question

1. find x if (overline{cb}=4x - 4) and (overline{xb}=x + 2).
2. find x if (overline{lm}=5x - 1) and (overline{xm}=x + 7).

Explanation:

Step1: Use the property of the median in a triangle

In a triangle, the median divides the opposite side into two equal parts. So, \(CB = 2XB\).
Given \(CB = 4x - 4\) and \(XB=x + 2\), we substitute into the equation \(4x-4=2(x + 2)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(4x-4 = 2x+4\).

Step3: Move the \(x\) terms to one side and constants to the other side

Subtract \(2x\) from both sides: \(4x-2x-4=2x - 2x+4\), which simplifies to \(2x-4 = 4\).
Then add \(4\) to both sides: \(2x-4 + 4=4 + 4\), so \(2x=8\).

Step4: Solve for \(x\)

Divide both sides by \(2\): \(x=\frac{8}{2}=4\).

Step1: Use the property of the median in a triangle

In a triangle, the median divides the opposite side into two equal parts. So, \(LM = 2XM\).
Given \(LM = 5x - 1\) and \(XM=x + 7\), we substitute into the equation \(5x-1=2(x + 7)\).

Step2: Expand the right - hand side

Using the distributive property \(a(b + c)=ab+ac\), we have \(5x-1 = 2x+14\).

Step3: Move the \(x\) terms to one side and constants to the other side

Subtract \(2x\) from both sides: \(5x-2x-1=2x - 2x+14\), which simplifies to \(3x-1 = 14\).
Then add \(1\) to both sides: \(3x-1 + 1=14 + 1\), so \(3x=15\).

Step4: Solve for \(x\)

Divide both sides by \(3\): \(x=\frac{15}{3}=5\).

Answer:

\(4\)