You need to bring the terms to a common denominator, such that:

`8 + 18/w = 14 => 8w + 18 = 14w`

You need to isolate the terms that contain w to one side, such that:

`18 = 14w - 8w => 18 = 6w => w = 18/6 => w = 3`

Since `w!=0` , hence `w = 3` is a valid value.

**Hence, evaluating `w` , under the given conditions, yields `w = 3` .**

The equation 8+18/w=14 has to be solved for the variable which here refers to w.

8+18/w=14

Add -8 to both the sides

8+18/w - 8 = 14 - 8

18/w = 6

Divide both the sides by 6

(18/w)/6 = 6/6

3/w = 1

Multiply both the sides by w

(3/w)*w = 1*w

3 = w

The solution of the equation is w = 3

We'll start wtih the original equation:

8+18/w=14

We'll subtract 8 from both sides:

18/w = 14 - 8

We'll combine like terms from the right side:

18/w = 6

We'll cross multiply:

18 = 6w

We'll divide by 6 both sides and we'll use symmetric property:

w = 3

The value of the variable w that verifies the given equation is w = 3.