Blue Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical expression that shows the relationship between two expressions using an inequality sign (such as <, >, ≤, or ≥) instead of an equals sign.

Front

How do you represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a line that divides the coordinate plane into two regions, with one region shaded to indicate the solutions of the inequality.

Front

What does the shaded area in a graph of a linear inequality represent?

Back

The shaded area represents all the possible solutions to the inequality.

Front

What is the difference between a solid line and a dashed line in the graph of a linear inequality?

Back

A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

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

Back

To determine if a point is a solution, substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the standard form of a linear inequality in two variables?

Back

The standard form of a linear inequality in two variables is Ax + By <, >, ≤, or ≥ C, where A, B, and C are constants.

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 does the inequality 3x + 7y ≥ 400 represent in a word problem context?

Back

It represents a situation where the total sales from selling x small bags at $3 and y large bags at $7 must be at least $400.

Front

What is the significance of the coefficients in a linear inequality?

Back

The coefficients represent the rate of change or contribution of each variable to the total value of the inequality.

Front

How do you graph the inequality 10 ≥ x?

Back

Graph the line x = 10 as a solid line and shade to the left to indicate that x can take any value less than or equal to 10.