Question

AB=5,BC=3x+7,AC=5x−2Find the value of x if A, B, and C are collinear points and B is between A and C.AB=5,BC=3x+7,AC=5x−2

Answer 1

Collinear points are points that all lie in the same line.

Given system is representied in the image above.

AB+BC=AC

Use the given data to write an equation in terms of x:

`\begin{gathered} AB+BC=AC \\ \\ 5+3x+7=5x-2 \end{gathered}`

Use the equation above to solve x:

`\begin{gathered} 12+3x=5x-2 \\ 12-12+3x=5x-2-12 \\ 3x=5x-14 \\ 3x-5x=5x-5x-14 \\ -2x=-14 \\ (-2)/(-2)x=(-14)/(-2) \\ x=7 \\ \end{gathered}`

Then, the value of x is 7