Question

1. given that a, b, and c are collinear points, and ac=10x−4, ab=5x+3, and bc=3x−1. find the value of x.

a) x=5
a) x=4
c) x=3
d) x=2
∘ a) x=5
∘ a) x=4
∘ c) x=3
∘ d) x=3

Explanation:

Step1: Determine the segment addition

Since A, B, C are collinear and B is between A and C, we have \( AB + BC = AC \).
Substitute the given expressions: \( (5x + 3) + (3x - 1) = 10x - 4 \).

Step2: Simplify the left side

Combine like terms: \( 5x + 3 + 3x - 1 = 8x + 2 \).
So the equation becomes \( 8x + 2 = 10x - 4 \).

Step3: Solve for x

Subtract \( 8x \) from both sides: \( 2 = 2x - 4 \).
Add 4 to both sides: \( 6 = 2x \).
Divide by 2: \( x = 3 \).

Answer:

C) \( x = 3 \)