9th grade mathematics

Front

What is a solution set in mathematics?

Back

A solution set is the set of all values that satisfy a given mathematical equation or inequality.

Front

What does it mean for a point to be part of a solution set?

Back

A point is part of a solution set if it satisfies the equation or inequality defined by the problem.

Front

How do you write a linear inequality in standard form?

Back

A linear inequality in standard form is typically written as Ax + By ≤ C or Ax + By ≥ C, where A, B, and C are constants.

Front

What is the difference between '<' and '≤' in inequalities?

Back

The symbol '<' means 'less than' and does not include the endpoint, while '≤' means 'less than or equal to' and includes the endpoint.

Front

What does the graph of an inequality represent?

Back

The graph of an inequality represents all the solutions that satisfy the inequality, often shown as a shaded region.

Front

How do you determine if a point is a solution to an inequality?

Back

To determine if a point is a solution to an inequality, substitute the point's coordinates into the inequality and check if the statement is true.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the points where the inequality changes from true to false; it is solid for '≤' or '≥' and dashed for '<' or '>'.

Front

What does the term 'at least' indicate in a mathematical context?

Back

The term 'at least' indicates a minimum value that must be met or exceeded, often represented by a '≥' inequality.

Front

How can you convert a word problem into a linear inequality?

Back

Identify the quantities involved, determine the relationship between them, and express the conditions using inequality symbols.

Front

What is the standard form of a linear equation?

Back

The standard form of a linear equation is Ax + By = C, where A, B, and C are integers.