Point C is on line segment overline (BD) Given CD=x,BC=5x-5 and BD=2x+7 determine the numerical length of overline (CD) Answer Attemptiout of? CD=square

Here's how to solve for the length of CD:<br /><br />1. **Understand the relationship:** Since C is on line segment BD, we know that BC + CD = BD.<br /><br />2. **Substitute the given values:** We are given CD = x, BC = 5x - 5, and BD = 2x + 7. Substituting these into the equation from step 1 gives us: (5x - 5) + x = 2x + 7<br /><br />3. **Simplify and solve for x:**<br /> * Combine like terms on the left side: 6x - 5 = 2x + 7<br /> * Subtract 2x from both sides: 4x - 5 = 7<br /> * Add 5 to both sides: 4x = 12<br /> * Divide both sides by 4: x = 3<br /><br />4. **Find CD:** Since CD = x, and we found x = 3, then CD = 3.<br /><br />Therefore, the numerical length of $\overline{CD}$ is 3.<br /><br />Final Answer: The final answer is $\boxed{3}$<br />