System of Linear Inequalities Word Problems Part 1

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 region of solutions on a graph.

Front

How do you write a linear inequality from a word problem?

Back

Identify the quantities involved, assign variables, determine the relationship (greater than, less than, etc.), and express it in the form of an inequality.

Front

What does the symbol '<' represent in a linear inequality?

Back

The symbol '<' indicates that the left side is less than the right side, meaning the values on the left do not reach the value on the right.

Front

What does the symbol '>' represent in a linear inequality?

Back

The symbol '>' indicates that the left side is greater than the right side, meaning the values on the left exceed the value on the right.

Front

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

Back

The symbol '≤' indicates that the left side is less than or equal to the right side, meaning the values on the left can be equal to or less than the value on the right.

Front

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

Back

The symbol '≥' indicates that the left side is greater than or equal to the right side, meaning the values on the left can be equal to or exceed the value on the right.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a boundary line. 2. Use a dashed line for < or > and a solid line for ≤ or ≥. 3. Shade the region that satisfies the inequality.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is expressed as Ax + By <, >, ≤, or ≥ C, where A, B, and C are constants.

Front

In the inequality 14x + 5y < 1000, what do x and y represent?

Back

In this context, x represents the number of trees purchased, and y represents the number of bushes purchased.

Front

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

Back

Graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the feasible solutions.