Linear Inequalities- Word Problems

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 word problem as a linear inequality?

Back

Identify the variables, determine the relationship between them, and express the constraints using inequality symbols.

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

In the inequality 70x + 30 ≤ 500, what does 'x' represent?

Back

'x' represents the number of donuts Shirley can buy.

Front

How do you solve the inequality 125x + 55 < 600 for x?

Back

Subtract 55 from both sides to get 125x < 545, then divide by 125 to find x < 4.36.

Front

What is the first step in solving a linear inequality?

Back

Identify the variable and the inequality symbol, then isolate the variable on one side of the inequality.

Front

What is the significance of the constant term in a linear inequality?

Back

The constant term represents fixed costs or limits that affect the total outcome of the inequality.

Front

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

Back

Draw a number line, use an open circle for < or >, and a closed circle for ≤ or ≥, then shade the appropriate side.

Front

What does the solution set of a linear inequality represent?

Back

The solution set represents all possible values of the variable that satisfy the inequality.