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 k - 13 > -51?

Back

To solve k - 13 > -51, add 13 to both sides: k > -51 + 13, which simplifies to k > -38.

Front

What does a closed dot on a number line represent when graphing inequalities?

Back

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

Front

What does an open dot on a number line represent when graphing inequalities?

Back

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

Front

How do you graph the inequality x > 2?

Back

To graph x > 2, place an open dot at 2 on the number line and shade to the right to indicate all numbers greater than 2.

Front

What is the solution to the inequality 6x > 12?

Back

To solve 6x > 12, divide both sides by 6: x > 2.

Front

How do you solve the inequality -4d - 9 ≤ 3?

Back

To solve -4d - 9 ≤ 3, first add 9 to both sides: -4d ≤ 12, then divide by -4 (remember to flip the inequality): d ≥ -3.

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

What is the first step in solving an inequality?

Back

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