Solving 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 (>, <, ≥, ≤).

Front

What does the symbol '>' mean in an inequality?

Back

The symbol '>' means 'greater than'. It 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 '<' mean in an inequality?

Back

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

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

Back

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

Front

How do you solve the inequality x + 5 ≤ 13?

Back

Subtract 5 from both sides to get x ≤ 8.

Front

What is the solution set of the inequality 5z - 2 - 2z < 13?

Back

Combine like terms to get 3z - 2 < 13, then solve to find z < 5.

Front

Which point is a solution to the inequality y < 4x - 2?

Back

The point (1, 0) is a solution because it satisfies the inequality.

Front

How do you determine if a point is part of the solution set for 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 the solution set of an inequality represent?

Back

The solution set represents all the possible values that satisfy the inequality.