Question

find x if;· b is between a and c;· ab = x + 5;· bc = 2(x - 3); and· $overline{ab}congoverline{bc}$.

Explanation:

Step1: Set up the equation

Since $\overline{AB}\cong\overline{BC}$, we have $x + 5=2(x - 3)$.

Step2: Expand the right - hand side

Using the distributive property, $2(x - 3)=2x-6$. So the equation becomes $x + 5=2x-6$.

Step3: Move the $x$ terms to one side

Subtract $x$ from both sides: $x - x+ 5=2x - x-6$, which simplifies to $5=x - 6$.

Step4: Solve for $x$

Add 6 to both sides: $5 + 6=x-6 + 6$, so $x = 11$.

Answer:

$11$