One of the biggest challenges you may face when writing inequalities is determining which inequality symbol to use.

Match each situation with an inequality by dragging the inequality to the slot next to the situation. You may use some inequalities more than once or not at all.

Pause and Reflect

How can you tell if a situation involves less than?

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Situations involving less than have an upper limit, which is described using words such as fewer than, at most, or cannot exceed.

How can you tell if a situation involves greater than?

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Situations involving greater than have a lower limit, which is described using words such as at least, more than, or minimum.

How can you distinguish between situations involving less than and situations involving less than or equal to?

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If the boundary point, or upper limit, is included in the situation, we use "less than or equal to" to describe the situation. If not, we use "less than" instead.

Practice

Write an inequality representing each of the situations below.

1. Victor plans to walk at least 30 miles in a charity walk-a-thon. He has walked 12 miles so far. Write an inequality to determine how many more miles must Victor walk in order to meet his goal.

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   Is the limit an upper limit or a lower limit? Can the limit be a part of the set of possible values that makes the situation true?
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   12 + x ≥ 30
2. 12 more than a number is at most 30. Write an inequality to determine the number.

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   Is the limit an upper limit or a lower limit? Can the limit be a part of the set of possible values that makes the situation true?
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   12 + x ≤ 30
3. Roxanne spent $30 on a shirt at the mall and had no more than $12 left over. Write an inequality to determine the amount of money Roxanne took to the mall.

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   Is the limit an upper limit or a lower limit? Can the limit be a part of the set of possible values that makes the situation true?
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   x – 30 ≤ 12
4. Yvonne earned $12 per hour babysitting last weekend. She worked no less than 30 hours. Write an inequality to determine the amount of money Yvonne earned last weekend.

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   Is the limit an upper limit or a lower limit? Can the limit be a part of the set of possible values that makes the situation true?
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   12x ≥ 30