Question

1. given that d, e, and f are collinear, and df = 15x - 3, de = 7x + 5, and ef = 6x - 2. find the value of x. a) x = 3 b) x = 5 c) x = 6 d) x = 4

Explanation:

Step1: Use collinear - point property

Since D, E, and F are collinear, \(DE + EF=DF\).
Substitute the given expressions: \((7x + 5)+(6x-2)=15x - 3\).

Step2: Simplify the left - hand side

Combine like terms: \(7x+6x + 5 - 2=13x + 3\). So, \(13x+3 = 15x-3\).

Step3: Solve for x

Subtract \(13x\) from both sides: \(3=15x - 13x-3\), which simplifies to \(3 = 2x-3\).
Add 3 to both sides: \(3 + 3=2x\), so \(6 = 2x\).
Divide both sides by 2: \(x = 3\).

Answer:

A. \(x = 3\)