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Write a compound inequality to describe the following situation.

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

Short Answer

Expert verified

The compound inequality to describe the given situation is 5≤x≤15

Step by step solution

01

– 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≥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≤15.

02

– Rewrite the inequalities to as a compound inequality

Inequality for at least situation is x≥5]and inequality for at most situation is x≤15.

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

x≥5 and x≤15

5≤x≤15

03

– Final compound inequality

Therefore, the compound inequality to describe the given situation is 5≤x≤15.

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