Answer:
The numerical length of AC is;
[tex]15\text{ units}[/tex]Explanation:
Given that point B is on the line segment AC;
So,
[tex]AC=AB+BC[/tex]Given;
[tex]\begin{gathered} AC=5x+10 \\ AB=3x \\ BC=4x+8 \end{gathered}[/tex]substituting;
[tex]\begin{gathered} AC=AB+BC \\ 5x+10=3x+4x+8 \\ 5x+10=7x+8 \end{gathered}[/tex]solving for x, we have;
[tex]\begin{gathered} 5x+10=7x+8 \\ \text{subtract 8 from both sides;} \\ 5x+10-8=7x+8-8 \\ 5x+2=7x \\ \text{subtract 5x from both sides;} \\ 5x-5x+2=7x-5x \\ 2=2x \\ 2x=2 \\ \text{divide both sides by 2;} \\ \frac{2x}{2}=\frac{2}{2} \\ x=1 \end{gathered}[/tex]Since we have derived the value of x, let us substitute the value of x to get AC;
[tex]\begin{gathered} AC=5x+10 \\ AC=5(1)+10 \\ AC=15 \end{gathered}[/tex]Therefore, the numerical length of AC is;
[tex]15\text{ units}[/tex]
