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 $a(b - c)=ab - ac$, we get $x + 5 = 2x-6$.

Step3: Isolate the variable terms

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:

$11$