Linear Inequalities Flashcard

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 (such as <, >, ≤, or ≥).

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How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). Then shade the region that satisfies the inequality.

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the values of the variable can be less than or equal to a certain number.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the values of the variable can be greater than or equal to a certain number.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy 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 set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the graphical representation of the inequality y < -x + 5?

Back

The graph of y < -x + 5 is a dashed line with a slope of -1 and a y-intercept of 5, with the area below the line shaded.

Front

What does it mean if a point lies above the line in a graph of a linear inequality?

Back

If a point lies above the line in a graph of a linear inequality, it means that the point does not satisfy the inequality.