Question

What’s the algebraic expression for “the quantity x plus 9 times the quantity 7 minus x”?

Answer 1

Hint: First understand the definition of an algebraic expression using examples. Now, assume the required algebraic expression as y. Subtract x from 7 and place it inside the bracket. In the next step multiply this term with 9 and in the last step add the term x with the obtained product. Simplify the expression using simple arithmetic operations to get the answer.

Complete step by step solution:
Here we have been provided with the sentence “the quantity x plus 9 times the quantity 7 minus x” and we are asked to convert it into an algebraic expression. But first we need to understand the term ‘algebraic expression’.
In mathematics, an algebraic expression is an expression that contains constants, variables and algebraic operations like: - addition, subtraction, multiplication, division and exponentiation by an exponent that is a rational number. For example: - \[5{{x}^{3}}-3{{x}^{2}}y+xy+10\] is an algebraic expression.
Let us come to the question. We have to write the algebraic expression for the sentence: - the quantity x plus 9 times the quantity 7 minus x. Let as assume the expression as y.
Now first we need to take the difference of 7 and x where x will be subtracted from 7, so we get,
\[\Rightarrow 7-x\]
In the next step we need to multiply this term with 9 therefore we have to consider the bracket as both the terms will be multiplied with 9, so we get,
\[\Rightarrow 9\left( 7-x \right)\]
Finally we have to add the above product with x, so we get,
\[\Rightarrow y=x+9\left( 7-x \right)\]
On simplification we get,
\[\begin{align}
  & \Rightarrow y=x+63-9x \\
 & \therefore y=63-8x \\
\end{align}\]
Hence, the above algebraic expression is our answer.

Note: One may note that we must not substitute the obtained algebraic expression equal to 0. This is because if we do so then the algebraic expression will become an algebraic equation. Understand the words of the question carefully or otherwise you may make a mistake in including the required arithmetic operations which may lead to the wrong expression and hence the answer will be wrong.