Question

points a, b, and c are collinear. point b is between a and c. find the length indicated. 12) find ac if bc = 2x + 30, ab = 3, and ac = x + 22. find ac

Explanation:

Step1: Use segment - addition postulate

Since points A, B, and C are collinear and B is between A and C, we have $AB + BC=AC$. Given $BC = 2x + 30$, $AB = 3$, and $AC=x + 22$, we substitute these values into the equation: $3+(2x + 30)=x + 22$.

Step2: Simplify the left - hand side of the equation

Combine like terms on the left - hand side: $3+2x+30=2x + 33$. So the equation becomes $2x+33=x + 22$.

Step3: Solve for x

Subtract x from both sides: $2x - x+33=x - x + 22$, which simplifies to $x+33 = 22$. Then subtract 33 from both sides: $x=22 - 33=-11$.

Step4: Find the length of AC

Substitute $x=-11$ into the expression for AC. Since $AC=x + 22$, then $AC=-11 + 22 = 11$.

Answer:

11