Question

What is the algebraic expression for the product of \[8\] and a number k is greater than \[4\] and not more than \[16\]?

Answer 1

Hint: First we need to obtain the necessary conditions from the given information. In this question, we have two numbers and two relations. We have to find out the algebraic expression between them. We have to first write the product of two numbers. Then considering the relations less than and greater than accordingly, we will get the required algebraic expression.

Complete step-by-step solution:
We need to find out the algebraic expression for the product of \[8\] and a number k is greater than \[4\] and not more than \[16\].
First, we need to find the product of \[8\] and a number k which is \[8 \times k = 8k\]
Now we need to consider \[8k\] is greater than \[4\] and not more than \[16\].
We know that, less than is symbolised as < and greater than is symbolised as $>$.
Thus, a is less than b can be symbolically represented as \[a < b\] and c is greater than d can be symbolically denoted as \[c > d\].
Therefore by considering \[8k\] is greater than \[4\] and not more than \[16\],we get,
\[4 < 8k < 16\]
Hence the required algebraic expression is,
\[4 < 8k < 16\]

Note: Algebraic expression:
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and the algebraic operations.
For example,
\[{x^2} + 6xy + 7\] is an algebraic expression where \[7\]is an integer constant and x and y are the variables and + is the algebraic operation.
Algebraic equation:
In mathematics, an algebraic equation is a mathematical statement in which two expressions are set equal to each other.
For example we can take \[a{x^2} + bx + c = 0\]as an algebraic equation.