Question

How do you write six less than seven times a number is equal to $-20$ as an equation? What is the number?

Answer 1

Hint: In the above question, we have been given a mathematical statement which we have been asked to convert into a mathematical equation. The statement is about an unknown number, six less than seven times of which is equal to $-20$. Firstly, we have to represent the unknown number by a variable, say x. The term “less than” refers to subtraction, and “times” refers to the multiplication. Therefore, seven into x minus six will be equal to $-20$, according to the given statement. On writing this statement mathematically, we will obtain the required mathematical equation of the given statement. On solving the mathematical equation for x, we will get the required value for the unknown number.

Complete step by step answer:
The statement given to us in the above question states that “less than seven times a number is equal to $-20$”. Since the given statement is focused on an unknown number, we have to represent it by a variable, say x. So the statement now becomes six less than seven into x is equal to $-20$. Now, we know that the term “less than” refers to the subtraction operation, and “times” refers to the multiplication. So finally we can write the mathematical equation as
$\Rightarrow 7x-6=-20$
On adding $6$ both sides of the above equation, we get
$\begin{align}
  & \Rightarrow 7x-6+6=-20+6 \\
 & \Rightarrow 7x=-14 \\
\end{align}$
Finally, on dividing both the sides of the above equation by, $7$ we get
$\begin{align}
  & \Rightarrow \dfrac{7x}{7}=\dfrac{-14}{7} \\
 & \Rightarrow x=-2 \\
\end{align}$

Hence, the unknown number is equal to $-2$.

Note: Read the statement very carefully and do not ignore any of the terms present in the statement. Each term has its own significance. You can check the correctness of the equation by translating your equation back into the statement and comparing it with the given statement.