Solving Inequalities and Graphing

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

How do you solve the inequality 28 - k ≥ 7(k - 4)?

Back

First, distribute: 28 - k ≥ 7k - 28. Then, combine like terms: 28 + 28 ≥ 7k + k. This simplifies to 56 ≥ 8k, or k ≤ 7.

Front

What does the inequality x < 8 mean?

Back

It means that x can be any number less than 8.

Front

Which numbers satisfy the inequality x < 8?

Back

Examples include 0.8, 5.9, and 7.9.

Front

How do you graph the inequality r ≥ -6?

Back

You use a closed circle at -6 and shade to the right to indicate all numbers greater than or equal to -6.

Front

What type of circle is used to graph x < 3?

Back

An open circle is used to indicate that 3 is not included in the solution.

Front

How do you solve the inequality 4x - 2 ≤ -22?

Back

Add 2 to both sides: 4x ≤ -20. Then divide by 4: x ≤ -5.

Front

What is the solution set for the inequality k ≤ 7?

Back

The solution set includes all numbers less than or equal to 7.

Front

What does it mean if an inequality has a closed circle on a number line?

Back

It means that the number is included in the solution set.

Front

What does it mean if an inequality has an open circle on a number line?

Back

It means that the number is not included in the solution set.