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

Front

What does the symbol '≥' mean 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

How do you graph the inequality y ≥ -3?

Back

To graph y ≥ -3, draw a horizontal line at y = -3 and shade the area above the line, including the line itself.

Front

Which points are part of the solution set for the inequality y < 2?

Back

Points that lie below the line y = 2 are part of the solution set.

Front

What does the solution set of a linear inequality represent?

Back

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

Front

How do you determine if a point is in the solution set of an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means 'greater than' (not including the boundary), while '≥' means 'greater than or equal to' (including the boundary).

Front

How do you solve the inequality 5x + y ≤ -1 for y?

Back

Rearranging gives y ≤ -5x - 1.

Front

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

Back

The graph is a line with a slope of 2/5, where the area below the line is shaded, including the line itself.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it is included in the solution set if the inequality is '≥' or '≤', but not if it is '>' or '<'.