Inequalities and Inverse Operations

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 symbols are used to represent inequalities?

Back

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

Front

How do you solve the inequality t + 8 > 30?

Back

To solve the inequality, subtract 8 from both sides: t > 30 - 8, which simplifies to t > 22.

Front

What does a closed dot on a graph indicate when graphing inequalities?

Back

A closed dot indicates that the value is included in the solution set, used for inequalities with ≤ or ≥.

Front

What does an open dot on a graph indicate when graphing inequalities?

Back

An open dot indicates that the value is not included in the solution set, used for inequalities with < or >.

Front

How do you determine if a value satisfies an inequality?

Back

To determine if a value satisfies an inequality, substitute the value into the inequality and check if the statement is true.

Front

What is the solution to the expression x + 18 when x = 6?

Back

The solution is 24, as you substitute 6 for x: 6 + 18 = 24.

Front

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

Back

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

Front

How do you graph the inequality x < 5?

Back

To graph x < 5, draw a number line, place an open dot at 5, and shade to the left to indicate all values less than 5.

Front

What is the first step in solving the inequality 3x - 4 ≤ 11?

Back

The first step is to add 4 to both sides: 3x ≤ 11 + 4, which simplifies to 3x ≤ 15.