A.3D

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 (such as <, >, ≤, or ≥). It represents a region of solutions on a graph.

Front

How do you write a linear inequality from a word problem?

Back

Identify the variables, determine the constraints, and express the relationship using an inequality symbol. For example, '3x + 5y ≤ 480' represents the manufacturing hours constraint.

Front

What does the solution set of an inequality represent?

Back

The solution set of an inequality represents all the ordered pairs (x, y) that satisfy the inequality, forming a region on a graph.

Front

What is the graphical representation of a linear inequality?

Back

The graphical representation of a linear inequality is a shaded region on one side of the boundary line, which is either solid (for ≤ or ≥) or dashed (for < or >).

Front

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

Back

Substitute the values of the ordered pair into the inequality. If the inequality holds true, then the ordered pair is a solution.

Front

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

Back

The boundary line represents the values where the inequality changes from true to false. It is included in the solution set if the inequality is ≤ or ≥.

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 does the symbol '<' mean in an inequality?

Back

The symbol '<' means 'less than', indicating that the value on the left is strictly less than the value on the right.

Front

How can you check if a point lies within the solution set of an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality is satisfied, the point lies within the solution set.

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is given by y = mx + b, where m is the slope and b is the y-intercept.