Unit 5: Flashcardziz #2: Writing 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 values rather than a single value.

Front

How do you write an inequality for a situation involving total cost?

Back

Identify the variables representing the quantities involved, assign values to each variable based on their costs, and use an inequality symbol to express the total cost in relation to a budget.

Front

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

Back

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

Front

How can you represent the total number of tickets sold in an inequality?

Back

Front

What is the first step in solving a linear inequality?

Back

The first step is to isolate the variable on one side of the inequality by performing inverse operations, similar to solving an equation.

Front

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

Back

To graph a linear inequality, first graph the corresponding equation as a line. Use a solid line for '≤' or '≥' and a dashed line for '<' or '>'. Then shade the region that satisfies the inequality.

Front

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

Back

The symbol '<' means 'less than' and does not include the value, while '≤' means 'less than or equal to' and includes the value.

Front

How do you write an inequality for a budget constraint?

Back

Identify the total budget and the costs associated with each item. Use variables to represent the quantities of each item and write an inequality that expresses the total cost in relation to the budget.

Front

What does the term 'solution set' mean in the context of inequalities?

Back

The solution set of an inequality is the set of all values that satisfy the inequality. It can be represented on a number line or in interval notation.

Front

How do you interpret the solution of an inequality in a real-world context?

Back

The solution of an inequality represents all possible values that meet the conditions of the problem, such as the maximum or minimum quantities allowed.