Question

Find the value of x if A, B, and C are collinear points and B is between A and C.

AB=5x−1,BC=14,AC=25−x

Answer 1

The value of x is:

`x=2`

Explanation:

Three points are said to be collinear if they lie along a straight line.

Also, it is given that:

Here A, B, and C are collinear points and B is between A and C.

This means that:

`AB+BC=AC-----------(1)`

Also we are given:

`AB=5x-1,\ BC=14,\ AC=25-x`

Using property (1) we have:

`5x-1+14=25-x\\\\i.e.\\\\5x+13=25-x`

Now on adding x on both the side of the equation we have:

`5x+13+x=25\\\\i.e.\\\\5x+x+13=25\\\\i.e.\\\\6x+13=25`

Now on subtracting 13 on both the sides of the equation we have:

`6x=25-13\\\\i.e.\\\\6x=12\\\\i.e.\\\\x=(12)/(6)\\\\i.e.\\\\x=2`

Answer 2

x = 2

Explanation:

Collinear means that the points A, B and C all lie in a straight line, hence

AB + BC = AC, substitute values

5x - 1 + 14 = 25 - x

5x + 13 = 25 - x ( add x to both sides )

6x + 13 = 25 ( subtract 13 from both sides )

6x = 12 ( divide both sides by 6 )

x = 2