Algebra I - 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 (>, <, ≥, ≤).

Front

What does the symbol '≥' mean in an inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the number.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid or dashed line. 2. Shade the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

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

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

The inequality sign flips (e.g., if you have -2x > 6, dividing by -2 changes it to x < -3).

Front

What is the solution set of an inequality?

Back

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

Front

How can you tell if an inequality will have a dashed line?

Back

If the inequality symbol is '>' or '<', the line will be dashed, indicating that points on the line are not included.

Front

What does it mean if an inequality has no solution?

Back

It means there are no values that can satisfy the inequality, often occurring when the inequality contradicts itself.

Front

What is the graphical representation of the inequality x < 3?

Back

A dashed vertical line at x = 3, with shading to the left, indicating all values less than 3.