Show all work to solve the equation for x. if a solution is extraneous, be sure to identify it in your final answer.

square root of the quantity x minus 3 end quantity plus 5 equals x

There is one extraneous solution at

The only solution is

Step-by-step explanation:

Given:

The equation to solve is given as:

In order to solve, we will first isolate the radical part.

Adding -5 on both the sides, we get:

Now, squaring both the sides, we get:

Now, let us check whether the calculated values satisfy the equations or not.

Plug in 4 and 7 for 'x' and check the value of the equation.

At ,

But, 6 is not equal to 4 and hence 4 is not a solution to the given equation. It is an extraneous solution for the given equation.

Now, at

Therefore, is a solution to the equation.

Hence, there is one extraneous solution at

The only solution is

question: how many people can she serve?

answer: she can serve 16.66666667 people. so she can only give 16 people a complete serving.

question: does she have enough ice cream for her guests?

answer: no. explanation: she only has enough for 16 people to have a full serving. however, she can give a 17th person a partial serving.