Equations and 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, or not equal to the other. Examples include: x < 5, y ≥ 3.

Front

What does the symbol '≤' mean?

Back

The symbol '≤' means 'less than or equal to'. It indicates that a value can be either less than or exactly equal to another value.

Front

What does the symbol '≥' mean?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that a value can be either greater than or exactly equal to another value.

Front

How do you solve the equation m - 13 = 33?

Back

To solve for m, add 13 to both sides of the equation: m = 33 + 13, so m = 46.

Front

What is the solution to the equation 2t = 20?

Back

To solve for t, divide both sides by 2: t = 20 / 2, so t = 10.

Front

What does an open circle on a number line represent?

Back

An open circle on a number line indicates that the endpoint is not included in the solution set. For example, x < 4 is represented with an open circle at 4.

Front

What does a closed circle on a number line represent?

Back

A closed circle on a number line indicates that the endpoint is included in the solution set. For example, x ≤ 4 is represented with a closed circle at 4.

Front

What is the first step in solving the inequality x < 4?

Back

The first step is to identify the boundary point, which is 4, and then determine the values that are less than 4.

Front

How do you graph the inequality x ≥ -4?

Back

To graph x ≥ -4, place a closed circle at -4 and shade to the right to indicate all values greater than or equal to -4.

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.