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.

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSA.REI.D.12

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 >).

Tags

CCSS.HSA.REI.D.12

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.

Tags

CCSS.HSF.LE.B.5

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.

Tags

CCSS.HSA.REI.D.12