Question

How do you express the sum of a number times 6 and 19 are at most 22?

Answer 1

Hint: Assume the number as variable x. Take the product of this variable assumed with 6 and add the result with the given numerical value 19. Now, understand the meaning of the term ‘at most’. Write the expression that was obtained in the initial stage in the L.H.S. and use the symbol ‘\[\le \]’, then in the R.H.S. write 22. The obtained algebraic inequality will be our answer.

Complete step by step answer:
Here, we have been provided with the sentence ‘the sum of a number times 6 and 19 is at most 22’ and we have been asked to write an algebraic expression for this sentence.
Now, let us assume the number as variable ‘x’. It is said that we are taking 6 times this number, so taking the product of this variable with 6, we have 6x. In the next step, we are taking the sum of this product and the given numerical value 19. So, the expression becomes,
\[\Rightarrow 6x+19\]
Now, it is said that the value of this expression is at most 22. That means the value cannot be greater than 22 but it can be less than or equal to 22. This is an inequality condition and we use the mathematical symbol ‘\[\le \]’ for such cases. So, considering (6x + 19) in the L.H.S. and 22 in the R.H.S., we get,
\[\Rightarrow 6x+19\le 22\]. Hence, the above expression is our answer.

Note:
One must know the difference between the terms ‘at most’ and ‘at least’ otherwise you will get confused and write the expression wrong. Note that if we would have been provided with the term ‘at least’ then we would have used the ‘\[\ge \]’ symbol for that case and the resultant expression would have been \[6x+19\ge 22\]. Remember that here we do not have to solve this inequality obtained in the solution. Note that the terms ‘at most’ and ‘at least’ are mostly used in chapter ‘probability’.