The sentence is one third equals negative seven times a number.

The word “times” indicates the symbol " "

The word “equals” indicates the symbol “”

The word “negative” indicates the symbol “"

Let = number.          

Rewrite the sentence into equation,

The equation is 

According to division property of equality: Divide each side by 7.

                     (Cancel common terms)

                           (Multiply: )

                 (Multiply each side by negative one)

                          (Product of two same signs is positive) \ \

Check:

To check the solution, substitute in original equation.

                              (Multiply:  )

Compare the values, the equation is true. The solution is .

The solution is .