Questions: Use the following information to find x. Write the value of the variable. [5 POINTS] NWNC! - B is between A and C; - AB=3x+6 - BC=15x-2 and - AB ≅ BC.

Transcript text: 6. Use the following information to find $x$. Write the value of the variable. [5 POINTS] NWNC! - $B$ is between $A$ and $C$; - $A B=3 x+6$ - $B C=15 x-2$ and - $\overline{A B} \cong \overline{B C}$.

Solution

Solution Steps

To find the value of $ x $, we need to use the given information that $ \overline{A B} \cong \overline{B C} $. This means that the lengths of $ AB $ and $ BC $ are equal. Therefore, we can set up the equation $ AB = BC $ and solve for $ x $.

Step 1: Set Up the Equation

Given that $ \overline{AB} \cong \overline{BC} $, we know that the lengths of $ AB $ and $ BC $ are equal. Therefore, we can set up the equation: \[ AB = BC \] Substituting the given expressions for $ AB $ and $ BC $: \[ 3x + 6 = 15x - 2 \]

Step 2: Solve for $ x $

To solve for $ x $, we first isolate $ x $ on one side of the equation. Subtract $ 3x $ from both sides: \[ 6 = 12x - 2 \] Next, add 2 to both sides: \[ 8 = 12x \] Finally, divide both sides by 12: \[ x = \frac{2}{3} \]

Final Answer

$\boxed{x = \frac{2}{3}}$

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