Solving Inequalities (Word Problems)

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using inequality symbols (>, <, ≥, ≤) to show that one expression is greater than, less than, or equal to another.

Front

What does it mean to solve an inequality?

Back

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

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality.

Front

How do you graph an inequality on a number line?

Back

To graph an inequality on a number line, use an open circle for < or > and a closed circle for ≤ or ≥, then shade the region that represents the solution set.

Front

What is the distributive property?

Back

The distributive property states that a(b + c) = ab + ac, allowing you to multiply a single term by two or more terms inside a set of parentheses.

Front

How do you apply the distributive property to simplify expressions?

Back

To apply the distributive property, multiply the term outside the parentheses by each term inside the parentheses.

Front

What is a linear inequality?

Back

A linear inequality is an inequality that involves a linear expression, typically in the form ax + b > c, where a, b, and c are constants.

Front

What is the difference between an equation and an inequality?

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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 solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality, similar to solving an equation, while remembering to reverse the inequality sign when multiplying or dividing by a negative number.

Front

What does it mean to 'isolate the variable'?

Back

Isolating the variable means to manipulate the equation or inequality so that the variable is on one side by itself.