Question

Write an inequality as a compound form and also draw a graph of it.“The ski wax you use keeps your skis performing well at temperaturefrom $-6°C to 15°C$ .Express the lower limit and upper limit of the skiwax”.

Short answer

The compound inequality of the situation is $-6°\le t\le 15°$.

Step-by-step solution

Step -1 - Apply the concept of Linear inequalities

In this type of question, Simply use the concept of understanding the question very carefully and then taking a variableand with accurate symbol >,< make a suitable inequality.

Step -2 – Find the inequality by explaining the statement

Here, The ski wax you use keeps your skis performing well at temperature from

$-6°C to 15°C$.

From the above statement, it is clearly seen that the wax need a minimum temperature of $-6°C$ and up to maximum temperature of $15°C$. So, the lower limit will be $-6°C$ and the upper limit will be $15°C$.

Step- 3 – Make the expression of the inequality

Now, Let t be the temperature range where the skis will perform well.

Then, the inequality of the two situation are: $t\ge -6°\&t\le 15°$

On combining the both inequality, it gives: $-6°\le t\le 15°$

Graphical Interpretation

Following is the graph of the expression $-6°\le t\le 15°$ to get the proper graphical representation to know the points.