Creating 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 ≥).

Front

How do you represent a budget constraint using a linear inequality?

Back

A budget constraint can be represented by a linear inequality that shows the total spending must be less than or equal to a certain amount.

Front

What does the symbol '<' mean 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 does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to' and indicates that the value on the left side is either greater than or equal to the value on the right side.

Front

How do you write an inequality for a situation where you want to spend less than a certain amount?

Back

You write an inequality using the '<' symbol to indicate that the total cost must be less than the specified amount.

Front

What is the significance of the coefficients in a linear inequality?

Back

The coefficients represent the cost or contribution of each variable to the total value being compared in the inequality.

Front

How do you determine the feasible region for a system of linear inequalities?

Back

The feasible region is determined by graphing the inequalities on a coordinate plane and identifying the area where all conditions are satisfied.

Front

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

Back

A linear equation shows equality (using =), while a linear inequality shows a relationship of less than, greater than, or equal to.

Front

How can you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality, similar to solving a linear equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does it mean if a linear inequality has no solution?

Back

If a linear inequality has no solution, it means that there are no values for the variables that satisfy all the conditions of the inequality.