Question

8 alexis was given the figure shown. she correctly solved to find the value of x. based on her work, determine the value of cb. cb = blank line segment with points a, c, b: ac = x+2, cb = 3x-9, ab = 6x-21. solving steps: x+2 + 3x-9 = 6x-21; 4x -7 = 6x -21; 14 = 2x; 7 = x

Explanation:

Step1: Analyze the equation from the work

From the work, we have the equation \(4x - 7=6x - 21\) (derived from the segment addition or equality, and then we also see steps like \(14 = 2x\) and \(7=x\)). Let's verify the solving of \(x\) first. Starting with \(4x - 7=6x - 21\), subtract \(4x\) from both sides: \(- 7=2x - 21\). Then add 21 to both sides: \(14 = 2x\), so \(x = 7\) (dividing both sides by 2).

Step2: Find the length of \(CB\)

The expression for \(CB\) is \(3x - 9\) (from the figure, the segment \(CB\) is labeled as \(3x - 9\)). Now substitute \(x = 7\) into this expression. So \(CB=3(7)-9\).

Step3: Calculate the value

First, calculate \(3\times7 = 21\), then \(21-9 = 12\).

Answer:

12