Solving linear inequalities in one variable

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 (like <, >, ≤, or ≥).

Front

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

Back

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

Front

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

Back

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

Front

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality using inverse operations, similar to solving an equation.

Front

What happens to the inequality sign when you multiply or divide by a negative number?

Back

When you multiply or divide both sides of an inequality by a negative number, you must reverse the inequality sign.

Front

Is -6 a solution to the inequality c + 7 < -2?

Back

Yes, -6 is a solution because when you substitute c with -6, the inequality becomes -6 + 7 < -2, which simplifies to 1 < -2 (false).

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that make the inequality true.

Front

What does it mean to graph a linear inequality?

Back

Graphing a linear inequality means representing the solution set on a number line or coordinate plane, using a dashed line for '<' or '>' and a solid line for '≤' or '≥'.

Front

What is the difference between '≤' and '<'?

Back

'≤' means 'less than or equal to', while '<' means 'less than' only. The former includes the boundary value, while the latter does not.

Front

What is a boundary line in the context of linear inequalities?

Back

A boundary line is the line that represents the equation of the inequality when the inequality is treated as an equation (e.g., y = mx + b).