inequalities

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 are the symbols used for inequalities?

Back

The symbols used for inequalities are: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Front

What does an open dot represent when graphing inequalities?

Back

An open dot represents that the value at that point is not included in the solution set, used for < and >.

Front

What does a closed dot represent when graphing inequalities?

Back

A closed dot represents that the value at that point is included in the solution set, used for ≤ and ≥.

Front

How do you solve the inequality -14x + 18 ≤ 116?

Back

To solve -14x + 18 ≤ 116, first subtract 18 from both sides to get -14x ≤ 98, then divide by -14 (remember to flip the inequality sign) to get x ≥ -7.

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 solve an inequality?

Back

To apply the distributive property to solve an inequality, distribute the term outside the parentheses to each term inside, then combine like terms and isolate the variable.

Front

What is the solution to the inequality b > 1?

Back

The solution to the inequality b > 1 is all values of b that are greater than 1.

Front

How do you graph the inequality x < 3?

Back

To graph the inequality x < 3, draw a number line, place an open dot at 3, and shade to the left to indicate all values less than 3.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary point, while non-strict inequalities (≤, ≥) do include the boundary point.