Question

solve for x.
$x=\square$
(round to one decimal place as needed. use a comma to separate answers as needed.)

Explanation:

Step1: Apply Angle Bisector Theorem

The Angle Bisector Theorem states that an angle bisector in a triangle divides the opposite side into segments proportional to the adjacent sides. For this triangle, this gives:
$$\frac{11x - 2}{6x} = \frac{5x}{4x}$$

Step2: Simplify the right-hand side

Cancel out $x$ (since $x
eq 0$, as side lengths can't be 0):
$$\frac{11x - 2}{6x} = \frac{5}{4}$$

Step3: Cross-multiply to eliminate fractions

Multiply both sides by $6x \times 4$ to clear denominators:
$$4(11x - 2) = 5 \times 6x$$

Step4: Expand and simplify the equation

Calculate each side and rearrange terms to isolate $x$:
$$44x - 8 = 30x$$
$$44x - 30x = 8$$
$$14x = 8$$

Step5: Solve for x

Divide both sides by 14 and simplify the fraction:
$$x = \frac{8}{14} = \frac{4}{7} \approx 0.6$$

Answer:

$x \approx 0.6$