Linear Inequalities Check

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 a linear inequality?

Back

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

Front

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

Back

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

Front

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

Back

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

Front

How do you determine if a point is part of the solution set for a linear inequality?

Back

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

Front

What is the solution set of a linear inequality?

Back

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

Front

What does it mean if a point is NOT part of the solution set?

Back

It means that when the coordinates of that point are substituted into the inequality, the inequality does not hold true.

Front

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

Back

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

Front

What is the first step in solving a linear inequality?

Back

Isolate the variable on one side of the inequality, similar to solving an equation.

Front

What does it mean to 'shade' a region when graphing inequalities?

Back

Shading indicates the area of the graph that represents all the solutions to the inequality.