A1H Review Unit 10

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥). It represents a region of the coordinate plane.

Front

How do you write a linear inequality in standard form?

Back

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

Front

What does the inequality 5x + 12y ≤ 100 represent in a real-world context?

Back

It represents a budget constraint where 'x' is the number of pizzas and 'y' is the number of orders of breadsticks, and the total cost cannot exceed $100.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all ordered pairs (x, y) that satisfy the inequality.

Front

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

Back

To determine if a point (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.

Front

What does the symbol '≥' mean in an 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

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

Back

The boundary line represents the points where the inequality becomes an equation. The region above or below the line indicates the solutions to the inequality.

Front

What does the inequality y ≥ 3x - 6 represent graphically?

Back

It represents the region above the line y = 3x - 6, including the line itself, where y values are greater than or equal to the corresponding x values.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the boundary line as solid (for ≤ or ≥) or dashed (for < or >), then shade the appropriate region based on the inequality.

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point in a two-dimensional space, where 'x' is the horizontal coordinate and 'y' is the vertical coordinate.