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How do you translate 6 less than or equal to x cubed into an algebraic expression?

Last updated date: 23rd Feb 2024
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IVSAT 2024
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Hint: We are given a statement as 6 less than or equal to x cube. We are asked to translate this into an algebraic expression. To do so we will learn what algebraic expression refers to. Then we will use the algebraic tool like \[\le ,\ge ,<,>,+,-,\div ,\times ,etc.\] to simplify or change the statement written into mathematical form.

Complete step by step answer:
We are given a statement as 6 less than or equal to x. We have to write it into an algebraic expression. Before we solve, we should know that algebra is the equation or expression we will build up from integer, constant variables and the various algebraic tools. So, as we have to find the algebraic expression it means we have to translate the statement “6 less than x cube” into a mathematical expression. Before, we move another step we will learn how to express the word used in the given statement into the mathematical term. Now, less than is represented by the symbol ‘<’. Here, a < b. It means a is less than b. For symbol ‘>’, for example, a > b, it means a is greater than b. Now, we have that less than or equal to, so the symbol \[\le \] means less than or equal if \[a\le b\] means a is less than or equal to b. There is another word cube, the cube of any term means the product of any term with itself three times. Cube of a means \[a\times a\times a.\] We can denote a cube as \[a\times a\times a\] or \[{{a}^{3}}.\] In a simple way, say we denote as \[{{a}^{3}}.\] Now, we are given that x is cubed. So, it is denoted as \[{{x}^{3}}.\] Now, we will work on our problem. We have that 6 less than or equal to x cubed. For less than or equal we use \[\le \] and for x cube we use \[{{x}^{3}}.\] So, our equation will be expressed as \[6\le {{x}^{3}}.\]

Note: There are more tools available to us like +, –, x, /. When we are asked that sum or addition of two terms then we use ‘+’. If we have a difference or subtraction of two terms, then we use ‘–‘. If we are mentioned as the product of a term, so we use ‘x’ and if we are given a division of two terms, then ‘/’ is used to translate it into an algebraic expression.