Question

points a, b, c, and d are collinear and positioned in that order. solve for x. 9) (ab = 2x + 30), (ad = x + 32), (cd = 8), and (bc = 5). find x.

Explanation:

Step1: Use collinear - point property

Since A, B, C, D are collinear, $AD=AB + BC+CD$.

Step2: Substitute given values

Substitute $AB = 2x + 30$, $AD=x + 32$, $CD = 8$, and $BC = 5$ into the equation:
$x + 32=(2x + 30)+5 + 8$.

Step3: Simplify the right - hand side

$x + 32=2x+43$.

Step4: Solve for x

Subtract x from both sides: $32=x + 43$. Then subtract 43 from both sides: $x=32 - 43=-11$.

Answer:

$x=-11$