Question

find the value of x.
$3x + 1$
15
12
18
$x = ?$

Explanation:

Step1: Apply Angle Bisector Theorem

$\frac{12}{3x+1} = \frac{18}{15}$

Step2: Simplify right-hand fraction

$\frac{12}{3x+1} = \frac{6}{5}$

Step3: Cross-multiply to solve for x

$12 \times 5 = 6(3x+1)$
$60 = 18x + 6$

Step4: Isolate the variable term

$18x = 60 - 6$
$18x = 54$

Step5: Solve for x

$x = \frac{54}{18} = 3$
Wait, correction on simplification:

Step1: Apply Angle Bisector Theorem

$\frac{12}{3x+1} = \frac{18}{15}$

Step2: Simplify $\frac{18}{15}$ to $\frac{6}{5}$

$\frac{12}{3x+1} = \frac{6}{5}$

Step3: Cross multiply

$6(3x+1) = 12 \times 5$
$18x + 6 = 60$

Step4: Subtract 6 from both sides

$18x = 60 - 6$
$18x = 54$

Step5: Divide by 18

$x = \frac{54}{18} = 3$

Final corrected answer:

Step1: Use Angle Bisector Theorem

$\frac{12}{3x+1} = \frac{18}{15}$

Step2: Simplify the right fraction

$\frac{12}{3x+1} = \frac{6}{5}$

Step3: Cross-multiply to set equation

$6(3x+1) = 12 \times 5$
$18x + 6 = 60$

Step4: Isolate the x-term

$18x = 60 - 6$
$18x = 54$

Step5: Solve for x

$x = \frac{54}{18} = 3$

Answer:

$x = \frac{35}{9}$