Question

How do you write the sentence as an algebraic equation: the product of three and the sum of a number and two is zero?

Answer 1

Hint: We first try to make the given written statement in its mathematical form. We assume variable $m$ for the summation. Then we multiply the sum with 3. We follow the multiplication process for signs and find the right sign for the multiplication. Then we equate it with 0. We get the mathematical statement as the solution.

Complete step by step answer:
The given statement is that we need to find the mathematical form of the expression which is the product of three and the sum of a number and two is zero.
We break the whole statement in two parts. In one part we do the summation and then in the second part we do the multiplication with 3.
We first assume one variable for the summation. Let the number be $m$. We have to find the summation of the number with 2.
Therefore, the algebraic form of the first part will be $\left( m+2 \right)$.
In the second part we need to find the multiplied value of the summation and the number 3
Therefore, we take the multiplication of 3 and $\left( m+2 \right)$ which is $3\times \left( m+2 \right)=3\left( m+2 \right)$
The final solution is equal to 0 which gives $3\left( m+2 \right)=0$.

Therefore, the final algebraic expression of the product of three and the sum of a number and two is zero is $3\left( m+2 \right)=0$.

Note: we can simplify the result and find the value of $m$ from the equation $3\left( m+2 \right)=0$.
$\begin{align}
  & 3\left( m+2 \right)=0 \\
 & \Rightarrow \left( m+2 \right)=0 \\
 & \Rightarrow m=-2 \\
\end{align}$
The value of the number is $-2$.