find the value of x. write your answer as a whole number or a decimal. x =

Explanation:

Step1: Apply the intersecting - chords theorem

If two chords $MN$ and $JL$ intersect at point $K$ inside a circle, then $MK\times KN=JK\times KL$. Here, $MK = 6$, $KN=x + 5$, $JK = 4$, and $KL=2x + 6$. So, we have the equation $6(x + 5)=4(2x + 6)$.

Step2: Expand both sides of the equation

Expand the left - hand side: $6(x + 5)=6x+30$. Expand the right - hand side: $4(2x + 6)=8x + 24$. So the equation becomes $6x+30 = 8x+24$.

Step3: Solve for $x$

Subtract $6x$ from both sides: $30=2x + 24$. Then subtract 24 from both sides: $2x=30 - 24=6$. Divide both sides by 2: $x = 3$.

Answer:

$3$