Chapter 1.4, Problem 16P

Tell whether the expressions in each pair are equivalent.

$4+6+x$ and $4\cdot x\cdot 6$

To determine

Whether the expressions $4+6+x$ and $4\cdot x\cdot 6$ are equivalent or not.

Answer to Problem 16P

The expression $4+6+x$ is not equivalent to expression $4+6+x$ .

Explanation of Solution

Given:

The expressions are $4+6+x$ and $4+6+x$

Calculation:

First expression is of addition. Add the expression as follows:

  $\begin{array}{l}\Rightarrow 4+6+x\\ \Rightarrow 10+x\end{array}$

Take the second expression and determine the product.

The product of second expression is calculated as follows:

  $\begin{array}{l}\Rightarrow 4\cdot x\cdot 6\\ \Rightarrow \left(6\cdot 4\right)x\\ \Rightarrow \left(\begin{array}{l}\underset{\_}{\begin{array}{l}6\\ \times 4\end{array}}\\ 24\end{array}\right)x\\ \Rightarrow 24x\end{array}$

Hence, both the expression is not same.

Thus, the expression $4+6+x$ is not equivalent to expression $4+6+x$ .