Linear Inequalities

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 ≥.

Front

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

Back

'≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What does the symbol '≤' represent in a linear inequality?

Back

'≤' means 'less than or equal to', indicating that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. 3. Shade the region that satisfies the inequality.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Front

What does a closed circle on a number line indicate?

Back

A closed circle indicates that the number is included in the solution set, used with '≤' or '≥'.

Front

What does an open circle on a number line indicate?

Back

An open circle indicates that the number is not included in the solution set, used with '<' or '>'.

Front

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

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation shows equality (e.g., y = mx + b), while a linear inequality shows a relationship of inequality (e.g., y < mx + b).

Front

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

Back

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