Linear Inequalities Word Problem Practice

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 where the total cost of items does not exceed a specified budget. For example, if items cost x and y, and the budget is B, the inequality is ax + by ≤ B.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to', indicating that the value on the left can be less than or equal to the value on the right.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left can be greater than or equal to the value on the right.

Front

How do you write an inequality for a situation where a student cannot spend more than $20 on snacks?

Back

The inequality would be 2.5x + 1.75y ≤ 20, where x is the number of hot chips and y is the number of sodas.

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, similar to solving an equation.

Front

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

Back

A linear equation states that two expressions are equal, while a linear inequality shows that one expression is less than, greater than, or not equal to another.

Front

How can you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, shade the region that satisfies the inequality (above or below the line).

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line, it satisfies the equation of the line, and whether it is included in the solution set depends on the inequality symbol (≤ or ≥ includes the line, < or > does not).

Front

How do you interpret the solution set of a linear inequality?

Back

The solution set of a linear inequality represents all possible combinations of values that satisfy the inequality, often visualized as a shaded region on a graph.