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 (such as <, >, ≤, or ≥).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions that satisfy the inequality, typically shown as a shaded region on one side of a boundary line.

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, the point is part of the solution set.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' represents a dashed line and does not include points on the line, while 'y ≤ mx + b' includes points on the line, represented by a solid line.

Front

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

Back

'≥' means 'greater than or equal to', indicating that the values can be equal to the boundary line.

Front

How do you graph the inequality y < 2x + 3?

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade below the line to represent all points where y is less than 2x + 3.

Front

What is the solution set of the inequality x > 4?

Back

The solution set includes all real numbers greater than 4, represented graphically as a line starting from 4 and extending to the right.

Front

What does the term 'boundary line' refer to in linear inequalities?

Back

The boundary line is the line that represents the equation of the inequality, which divides the graph into two regions.

Front

How do you solve the inequality 3x - 5 < 4?

Back

1. Add 5 to both sides: 3x < 9. 2. Divide by 3: x < 3.

Front

What is the significance of a dashed line in the graph of a linear inequality?

Back

A dashed line indicates that points on the line are not included in the solution set.