Question

A line segment is 26 centimeters long. If a segment, x centimeters, is taken, how much of the line segment remains? Translate into an equation.

Answer 1

Hint: First we need to understand the definition of an algebraic expression using examples. Now, consider the required algebraic expression as a linear equation in x. to find the required expression subtract x from the given numerical value 17. Take the exponent of x equal to 1.

Complete step by step answer:
Here we have been provided with a line segment of length 26 centimeters and a segment of length x centimeters is cut. We are asked to determine the length of the remaining portion. 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: - \[{{x}^{3}}-2x+8\] is an algebraic expression.
Now, there are certain types of algebraic expression based on integral exponents of the variables. For example: - an algebraic expression with exponent of the variable as 1 is called linear algebraic expression, like: - 2x + 5y + 6. If the exponent of the variable becomes 2 then it is called a quadratic algebraic expression, like: - \[{{x}^{2}}+x+1\]. Similarly, we name cubic expressions for the exponent 3 and bi-quadratic expressions for the exponent 4.
Let us come to the question. Clearly we are dealing with a line segment which has only one dimension (length), so the variable x will have the exponent equal to 1. Here we are cutting the length that means we need to subtract x from the entire length. Therefore, the expression we will get,
\[\therefore E=\left( 26-x \right)cm\], here E is the remaining length.

Note: One important thing that can be taken into account is that in the question we are asked to write an equation but actually we are forming an expression. You may note this difference between the terms ‘expression’ and ‘equation’. In general, if we just write a combination of constants and variables then it is called an expression and when we substitute this expression equal to 0 or any other numerical value then it becomes an equation.