Question

The sum of 3 times a number and 17 is fewer than 40

Answer 1

In this case, we are given a word problem about inequalities. We will write an inequation that represents the situation, and then, solve it.

Writing the inequality

For writing the inequation, we assume that when we are told "a number" it will represent a variable, in this example, x. So, we can write:

`3x+17<40`

As all the expresion must be fewer than 40, we used the symbol < (less than).

Solving the inequality

For solving the inequality, we clear out the variable x: we move out the number 17 to the right side by substracting, and the 3 by dividing, as shown:

`\begin{gathered} 3x+17<40 \\ 3x<40-17 \\ 3x<23 \\ x<(23)/(3) \end{gathered}`

This means that x must be less than 23/3 to hold the above condition.