Solving 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 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 4x + 1 > 13?

Back

To solve 4x + 1 > 13, subtract 1 from both sides to get 4x > 12, then divide by 4 to find x > 3.

Front

What does a closed dot on a number line indicate?

Back

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

Front

What does an open dot on a number line indicate?

Back

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

Front

How do you graph the inequality 5w ≥ 30 on a number line?

Back

First, solve for w: w ≥ 6. Then, place a closed dot at 6 and shade to the right to indicate all values greater than or equal to 6.

Front

What is the solution to the inequality -9x + 7 ≥ 25?

Back

To solve -9x + 7 ≥ 25, subtract 7 from both sides to get -9x ≥ 18, then divide by -9 (remember to flip the inequality) to find x ≤ -2.

Front

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

Back

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

Front

How do you represent the solution set of an inequality on a number line?

Back

The solution set is represented by a dot (open or closed) at the critical point and shading in the direction of the solution.

Front

What is the first step in solving an inequality?

Back

The first step is to isolate the variable on one side of the inequality, similar to solving an equation.