Question

Write a compound inequality to describe the following situation.

Buy a present that costs at least \(5 and at most \)15.

Short answer

The compound inequality to describe the given situation is $5\le x\le 15$

Step-by-step solution

– Define the inequality for at least and at most condition

Let the cost of the present is $x$.

The meaning of at least situation: to buy a present that costs at least $5 is as follows: The least is allowed to be 5; it can be 5 or any number greater than 5.

Inequality for at least situation is $x\ge 5$.

The meaning of at most situations: to buy a present that costs at most 15 is as follows: The most are allowed to be 15; it can be 15 or any number less than 15.

Inequality for at most situations is $x\le 15$.

– Rewrite the inequalities to as a compound inequality

Inequality for at least situation is $x\ge 5$]and inequality for at most situation is $x\le 15$.

Now, use the word ‘and’ and write the compound inequality then solve each inequality as follows:

$x\ge 5$ and $x\le 15$

$5\le x\le 15$

– Final compound inequality

Therefore, the compound inequality to describe the given situation is $5\le x\le 15$.