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 (>, <, ≥, ≤) instead of an equal sign.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value can be greater than or equal to a certain number.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the value can be less than or equal to a certain number.

Front

How do you determine if a line in a graph is solid or dashed?

Back

A solid line indicates that the inequality includes equality (≥ or ≤), while a dashed line indicates that the inequality does not include equality (> or <).

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you graph the inequality y < 2?

Back

To graph y < 2, draw a horizontal dashed line at y = 2 and shade the area below the line.

Front

What does the graph of x ≥ -1 look like?

Back

The graph of x ≥ -1 is a vertical solid line at x = -1, with shading to the right of the line.

Front

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

Back

'y < mx + b' uses a dashed line, while 'y ≤ mx + b' uses a solid line, indicating that the boundary line is not included in the first case but is included in the second.

Front

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

Back

Add 5 to both sides to get 3x < 9, then divide by 3 to find x < 3.

Front

What is the graphical representation of the inequality y ≥ -2/5x + 1?

Back

The graph has a solid line with a slope of -2/5 and a y-intercept of 1, shading above the line.