Question

By how much does $x$ exceed 17?\[\]

Answer 1

Hint: We recall the definition of variable constants and algebraic expression. We use the meaning of the word ‘exceed’ as ‘greater than’ and we express by how much the variable $x$ exceeds the constant 17 by finding their difference.\[\]

Complete step by step answer:
We know that an algebraic expression consists of variables whose values we do not know and constants whose value we know. The variable are commonly represented as by English small letters $x,y,z$ and the constants are numbers.\[\]
We know that the word ‘exceed’ is used when we compare two numerical quantities to state the larger quantity has become greater than the smaller quantity. For example the number of people in the stadium has exceeded 50,000. When we are asked by how much the larger quantity has exceeded the smaller quantity, we find the difference between the larger and smaller quantity by subtracting the smaller quantity from larger quantity.\[\]
We are asked in the question by how much does $x$ exceed 17. We see that when the question states $x$ has exceeded 17 which $x$ is larger than 17. Here the larger number is $x$ and the smaller number is 17. So we subtract the smaller number 17 from $x$ and find the answer as $x-17$. \[\]

Note: The obtained result $x-17$ is an algebraic expression with one variable and one constant. The power on the variable is called degree and here the degree is 1 and hence the expression is a linear expression. If the question would have asked how much $x$ falls short of 17 we would have subtracted $x$ from 17 and would have obtained the expression $17-x$.