Question

points a, b, and c are collinear. point b is between a and c. solve for x. 11) ac = 3x + 3, ab = -1 + 2x, and bc = 11. find x. 12) ac = 22, bc = x + 14, and ab = x + 10 find x.

Explanation:

Problem 11 (AC = 3x + 3, AB = -1 + 2x, BC = 11, B between A and C)

Step1: Use segment addition postulate

Since B is between A and C, \( AB + BC = AC \). Substitute the given expressions: \((-1 + 2x) + 11 = 3x + 3\)

Step2: Simplify left side

Combine like terms: \(2x + 10 = 3x + 3\)

Step3: Solve for x

Subtract \(2x\) from both sides: \(10 = x + 3\). Then subtract 3: \(x = 7\)

Problem 12 (AC = 22, BC = x + 14, AB = x + 10, B between A and C)

Step1: Use segment addition postulate

Since B is between A and C, \( AB + BC = AC \). Substitute the given expressions: \((x + 10) + (x + 14) = 22\)

Step2: Simplify left side

Combine like terms: \(2x + 24 = 22\)

Step3: Solve for x

Subtract 24: \(2x = -2\). Divide by 2: \(x = -1\)

Answer:

For problem 11: \( x = 7 \)
For problem 12: \( x = -1 \)