A.3D Synthesis - 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 (>, <, ≥, ≤) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed or solid line, then shade the region that satisfies the inequality.

Front

What does the symbol '>' represent in a linear inequality?

Back

The symbol '>' means 'greater than' and indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' represent in a linear inequality?

Back

The symbol '<' means 'less than' and indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What is the difference between a strict and a non-strict inequality?

Back

A strict inequality uses '>' or '<', while a non-strict inequality uses '≥' or '≤', which includes the boundary value.

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side using inverse operations, similar to solving an equation, while reversing the inequality sign if multiplying or dividing by a negative number.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all values that make the inequality true, often represented as an interval or a shaded region on a graph.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line represents the values where the inequality changes from true to false; it is solid for non-strict inequalities and dashed for strict inequalities.

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 coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is a compound inequality?

Back

A compound inequality combines two or more inequalities, often connected by 'and' or 'or', representing a range of values.