Question Point Cis on line segment overline (BD) Given CD=2x,BD=3x+4 and BC=2x-1 determine the numerical length of overline (BD) Answer Allemptiontof BD=square

To determine the numerical length of $\overline{BD}$, we need to use the given information about the lengths of $\overline{CD}$, $\overline{BC}$, and $\overline{BD}$.<br /><br />Given:<br />$CD = 2x$<br />$BD = 3x + 4$<br />$BC = 2x - 1$<br /><br />Since point C is on line segment $\overline{BD}$, we can write the equation:<br />$BC + CD = BD$<br /><br />Substituting the given values, we have:<br />$(2x - 1) + 2x = 3x + 4$<br /><br />Simplifying the equation, we get:<br />$4x - 1 = 3x + 4$<br /><br />Solving for $x$, we find:<br />$x = 5$<br /><br />Now, we can substitute the value of $x$ into the expression for $\overline{BD}$:<br />$BD = 3x + 4$<br />$BD = 3(5) + 4$<br />$BD = 15 + 4$<br />$BD = 19$<br /><br />Therefore, the numerical length of $\overline{BD}$ is 19.