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 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 boundary line. Use a solid line for ≤ or ≥ and a dashed line for < or >. Then shade the region that satisfies the inequality.

Front

What does it mean if a system of linear inequalities has no solution?

Back

A system of linear inequalities has no solution if the shaded regions of the inequalities do not overlap, indicating that there are no points that satisfy all inequalities simultaneously.

Front

What is the significance of the 'or equal to' in linear inequalities?

Back

The 'or equal to' indicates that points on the boundary line are included in the solution set, which is represented by a solid line in the graph.

Front

How do you determine if you need to flip the inequality sign when solving?

Back

You need to flip the inequality sign when you multiply or divide both sides of the inequality by a negative number.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality, often represented graphically as a shaded region on a number line or coordinate plane.

Front

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

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

Front

How can you check if a point is a solution to a linear inequality?

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To check if a point is a solution, substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What does the slope-intercept form of a linear equation look like?

Back

The slope-intercept form of a linear equation is written as y = mx + b, where m is the slope and b is the y-intercept.

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How do you find the y-intercept of a linear inequality?

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To find the y-intercept of a linear inequality, set x = 0 in the corresponding linear equation and solve for y.