Inequalities Word Problems

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions and shows that one is greater than, less than, greater than or equal to, or less than or equal to the other.

Front

What does it mean to solve an inequality?

Back

To solve an inequality means to find all the values of the variable that make the inequality true.

Front

What is the difference between an equation and an inequality?

Back

An equation states that two expressions are equal, while an inequality shows that one expression is greater than or less than another.

Front

How do you represent a situation where a person has a certain amount of money and is saving more?

Back

You can represent this situation with an equation or inequality that includes the initial amount and the amount saved over time.

Front

What is the general form of a linear inequality in one variable?

Back

The general form is ax + b < c, ax + b > c, ax + b ≤ c, or ax + b ≥ c, where a, b, and c are constants.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the appropriate side of the circle.

Front

What does the term 'at least' indicate in an inequality?

Back

The term 'at least' indicates that the value is greater than or equal to a certain number, represented as x ≥ a.

Front

What does the term 'no more than' indicate in an inequality?

Back

The term 'no more than' indicates that the value is less than or equal to a certain number, represented as x ≤ a.

Front

How do you solve an inequality involving subtraction?

Back

To solve an inequality involving subtraction, add the same number to both sides to isolate the variable.

Front

How do you solve an inequality involving multiplication?

Back

To solve an inequality involving multiplication, divide both sides by the same positive number. If you divide by a negative number, reverse the inequality sign.