Question

points a, b, and c are collinear. point b is between a and c. let ac = 16, ab = 2x + 33, and bc = x + 19. find x.

x = -1

x = 11

x = -12

x = -11

Explanation:

Step1: Apply collinear - point property

Since B is between A and C, $AB + BC=AC$. Substitute the given expressions: $(2x + 33)+(x + 19)=16$.

Step2: Combine like - terms

$2x+x+33 + 19=16$, which simplifies to $3x+52 = 16$.

Step3: Isolate the variable term

Subtract 52 from both sides: $3x=16 - 52$, so $3x=-36$.

Step4: Solve for x

Divide both sides by 3: $x=\frac{-36}{3}=-12$.

Answer:

$x = - 12$