Question

Six times a number is at least -24, how do you write the expression?

Answer 1

Hint: In this question, we are given a statement and we have to express it in mathematical form, for that we will take the help of algebra. Algebra is a branch of mathematics that is used in all the other branches; an algebraic expression is defined as a mathematical equation that contains both numerical values and alphabets. The alphabets in the algebraic expression represent some unknown quantity that is related to the constants in the algebraic expression. In the given question, “a number” is the unknown quantity so will represent it by an alphabet and express it in mathematical form by using the given information.

Complete step by step solution:
Let the number be “n”
Six times the number means that the number is added to itself 6 times or we can also say that the number is multiplied by 6, so 6 times of the number is written as –
$
  6 \times n \\
   \Rightarrow 6n \\
 $
Now, we are given that 6 times the number is at least 24, so it is written as –
$6n \geqslant - 24$
Hence six times a number is at least -24 is written as $6n \geqslant - 24$ .

Note: By the term “at least”, we mean that 6 times the number is either equal to -24 or greater than -24, that is, it cannot be smaller than -24. From the obtained expression, we can also find the possible values of x by dividing both the sides by 6 –
$
  \dfrac{{6n}}{6} \geqslant - \dfrac{{24}}{6} \\
  n \geqslant - 4 \\
 $
So, we get that the number is at least -4.