Chapter 1.1, Problem 40HP

To determine

To check: whether the Consuelo statement is true or James statement is true of the given variable expression.

Answer to Problem 40HP

Consuelo statement is true.

Explanation of Solution

Given:

The given variable expression is “three times the sum of n squared and 3”.

The Consuelo statement is $3\left(n^2+3\right)$ .

And the James statement is $3n^2+3$ .

Calculation:

The given variable expression is “three times the sum of n squared and 3”.

The algebraic expression of sum of n squared is $n^2$

Now, the sum of n squared and 3” is $n^2+3$ .

Therefore, the variable” three times the sum of n squared and 3” is written as $3\left(n^2+3\right)$

Now, the Consuelo statement is $3\left(n^2+3\right)$ , which is true.

And the James statement is $3n^2+3$ , which is false.

Hence, the Consuelo statement is true.