Activity 2.5 - Modeling 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 (such as <, >, ≤, or ≥). It represents a range of possible solutions rather than a single solution.

Front

How do you represent a real-world situation with a linear inequality?

Back

To represent a real-world situation with a linear inequality, identify the variables, determine the relationship between them, and express the constraints using an inequality.

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

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left side of the inequality is either smaller than or equal to 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 by performing inverse operations, similar to solving an equation. Remember to reverse the inequality sign if you multiply or divide by a negative number.

Front

What is the significance of the solution set of a linear inequality?

Back

The solution set of a linear inequality represents all the possible values of the variable that satisfy the inequality. It can be represented on a number line or in a graph.

Front

How do you graph a linear inequality on a number line?

Back

To graph a linear inequality on a number line, draw a solid dot for '≤' or '≥' and an open dot for '<' or '>'. Shade the region that represents the solution set.

Front

What is the difference between a linear equation and a linear inequality?

Back

A linear equation has a single solution, while a linear inequality has multiple solutions represented by a range of values.

Front

How do you interpret the slope in a linear inequality?

Back

The slope in a linear inequality indicates the rate of change of the dependent variable with respect to the independent variable. It shows how steep the line is and the direction of the relationship.

Front

What does it mean for a solution to be 'at least' a certain value in a linear inequality?

Back

'At least' means that the value can be equal to or greater than the specified value. In inequality terms, it is represented as '≥'.