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 (such as <, >, ≤, or ≥).

Front

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

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid or dashed line, then 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 that points on the line are not included (> or <).

Front

How can you tell if a linear inequality has a solid line?

Back

If the inequality symbol includes 'or equal to' (≥ or ≤), the line is solid.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By ≤ C, Ax + By ≥ C, Ax + By < C, or Ax + By > C, where A, B, and C are constants.

Front

What does the solution set of a linear inequality represent?

Back

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

Front

How do you determine the boundary line of a linear inequality?

Back

The boundary line is determined by converting the inequality into an equation (using = instead of <, >, ≤, or ≥) and graphing that line.

Front

What is the significance of the shaded region in the graph of a linear inequality?

Back

The shaded region represents all the possible solutions to the inequality.

Front

What does the inequality 'y < 2/5x + 1' represent graphically?

Back

It represents all the points below the line y = 2/5x + 1, not including the line itself.