Inequalities (8th Grade) - Period 6

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (such as <, >, ≤, ≥) to show that one expression is larger or smaller than the other.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

How do you represent a situation where a person has a certain amount of money and wants to keep at least a minimum amount after spending?

Back

You can represent this situation with an inequality. For example, if a person has $500 and wants to keep at least $200, the inequality would be: 500 - amount spent ≥ 200.

Front

What happens to the inequality symbol when you multiply or divide both sides by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must flip the inequality symbol.

Front

What is a solution to the inequality x < 8?

Back

Any number less than 8 is a solution. For example, 7, 0, and -3 are all solutions.

Front

How do you solve the inequality 5(6 + 3r) + 7 ≥ 127?

Back

First, simplify: 30 + 15r + 7 ≥ 127. Then, combine like terms: 15r + 37 ≥ 127. Subtract 37 from both sides: 15r ≥ 90. Finally, divide by 15: r ≥ 6.

Front

What is the first step in solving the inequality 2x + 3 < 11?

Back

The first step is to subtract 3 from both sides: 2x < 8.

Front

If you have the inequality 3x - 4 ≤ 5, how do you isolate x?

Back

Add 4 to both sides to get 3x ≤ 9, then divide by 3 to find x ≤ 3.

Front

What does the inequality 15 + 6x ≤ 100 represent in a real-world context?

Back

It represents a situation where a person is spending $15 plus $6 for each additional person, and they want to keep their total spending at or below $100.

Front

What are two examples of numbers that satisfy the inequality x > 5?

Back

Examples include 6 and 10, as both are greater than 5.