Question

How do you translate the word phrase into a variable expression: the product of 3 and a number decreased by 7?

Answer 1

Hint: We use the meaning of each word given in the expression and write the expression step-by-step according to the sequence of words given in the expression. Assume the number as any variable and form the expression.
* Product means the multiplication operation applied in between two or more values.
* Decreased means lowering the value or subtracting the value.

Complete step-by-step solution:
We have to form an expression for the statement: the product of 3 and a number decreased by 7
We use the definitions of product and decrease to form the expression.
Let us assume the number stated in the word phrase in the question as a variable.
Let the number be ‘x’............… (1)
Then the product of the number with 3 can be written as 3 multiplied with the number i.e. \[3 \times x\]
We can simply write the product of 3 with the number as \[3x\]..........… (2)
Now decrease the product of number obtained in equation (2) by 7
i.e. Subtract 7 from product of the number in equation (2) , i.e. \[\left( {3x - 7} \right)\]........… (3)

\[\therefore \]The expression: The product of 3 and a number decreased by 7 can be written as \[\left( {3x - 7} \right)\]

Note: Many students make mistake of writing the final answer as 3 multiplied by number minus 7 i.e. \[3(x - 7)\] which is wrong as here we have the product of 3 and a number as one thing and then decrease 7, but if it was a written product of 3 with the number decreased by 7 then we could’ve used this expression.