Grade 7 | Unit 6 | Lesson 14: Finding Solutions to Inequalities in Context | Practice Problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does the symbol '>' represent in inequalities?

Back

The symbol '>' means 'greater than'.

Front

What does the symbol '<' represent in inequalities?

Back

The symbol '<' means 'less than'.

Front

How do you solve the inequality 5 - 3x > 35?

Back

To solve the inequality, first subtract 5 from both sides to get -3x > 30, then divide by -3 (remember to flip the inequality sign) to get x < -10.

Front

What is the solution set for the inequality x > -10?

Back

The solution set for the inequality x > -10 includes all real numbers greater than -10.

Front

What does it mean for a solution to be 'correct' in the context of inequalities?

Back

A solution is 'correct' if it satisfies the inequality when substituted back into the original expression.

Front

In the context of the school band director's ticket pricing model, what does the expression 1000 - 50t represent?

Back

The expression 1000 - 50t represents the expected attendance at the concert based on the ticket price t.

Front

If the ticket price t is set at $8, what is the expected attendance according to the model?

Back

If t = 8, the expected attendance is 1000 - 50(8) = 1000 - 400 = 600.

Front

What is the significance of the statement 'the ticket price needs to be $8 or greater in order for at least 600 to attend'?

Back

This statement means that if the ticket price is less than $8, the expected attendance will drop below 600.

Front

How do you interpret the inequality -x - 6 > -3.5?

Back

To interpret the inequality, you can isolate x by adding 6 to both sides and then multiplying by -1, which gives x < 2.5.