Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

How do you represent the solution set of an inequality on a number line?

Back

You use a solid dot for '≥' or '≤' and an open dot for '>' or '<'. Then shade the appropriate direction.

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 graph the inequality y > 2?

Back

Draw a horizontal dashed line at y = 2 and shade the area above the line.

Front

What is the solution set for the inequality x < 3?

Back

The solution set includes all numbers less than 3, represented on a number line with an open dot at 3.

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

Back

If the boundary line is solid, the point is included in the solution set; if dashed, it is not included.

Front

How do you graph the inequality y ≤ -x + 2?

Back

Graph the line y = -x + 2 as a solid line and shade below the line.