Question

Consider the following equation+3二五年5+2Which row in the table is closest to the actual solution?

Answer 1

Answer:

the row in the table closest to the actual solution is x = 0.8

Step-by-step explanation:

Given:

`√(2x+3)\text{ = }(x)/(x+5)+2`

To find:

the row from the table of values is the one closest to the actual solution

Since we were not asked to use a particular method, we will be graphing the equation in order to get the actual solution. Then we will check the table for the row closest to it

Graphing the equation:

From the graph, the solution (point of intersection of both the left-hand side and the right-hand side) is (0.779, 2.135).

The actual solution we need to check for on the table is for x. The x value of the solution from the graph is 0.779

This means our solution is between the row x = 0.7 and x = 0.8

To determine the correct row, we will check for the difference in values of the expressions for x = 0.7 and x = 0.8

`\begin{gathered} when\text{ x = 0.7} \\ difference\text{ = 2.0976 - 2.1228} \\ difference\text{ = -0.0252} \\ \\ when\text{ x = 0.8} \\ difference\text{ = 2.1448 - 2.1379} \\ difference\text{ = 0.0069} \\ \\ For\text{ it to be close to the actual value, the value of the difference must be close to zero} \\ 0.0069\text{ is a closer value to zero that -0.0252} \end{gathered}`

Hence, the row in the table closest to the actual solution is x = 0.8