Unit 2 review - linear inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all ordered pairs (x, y) that make the inequality true.

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What does it mean if a system of inequalities has no solution?

Back

A system of inequalities has no solution if the shaded regions of the inequalities do not overlap, meaning there are no points that satisfy all inequalities simultaneously.

Front

What does it mean if a system of inequalities has an infinite number of solutions?

Back

A system of inequalities has an infinite number of solutions if the shaded regions overlap in such a way that there are infinitely many points that satisfy all inequalities.

Front

How do you determine if a point is a solution to a system of inequalities?

Back

To determine if a point is a solution, substitute the coordinates of the point into each inequality. If the point satisfies all inequalities, it is a solution.

Front

What is the standard form of a linear inequality?

Back

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

Front

What is the significance of the budget in the context of linear inequalities?

Back

The budget represents a constraint in a linear inequality, limiting the maximum amount that can be spent on items, which can be expressed as an inequality.