Solving Inequalities & Equations

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: < (less than), > (greater than), ≤ (less than or equal to), and ≥ (greater than or equal to).

Front

What does it mean to graph an inequality?

Back

Graphing an inequality involves representing the solutions of the inequality on a number line or coordinate plane, indicating which values satisfy the inequality.

Front

When graphing the inequality x < 3, what type of dot is used?

Back

An open dot is used when graphing x < 3, indicating that 3 is not included in the solution.

Front

When graphing the inequality x ≥ 2, what type of dot is used?

Back

A closed dot is used when graphing x ≥ 2, indicating that 2 is included in the solution.

Front

How do you solve the inequality 4x - 2 ≤ -10?

Back

To solve 4x - 2 ≤ -10, add 2 to both sides to get 4x ≤ -8, then divide by 4 to find x ≤ -2.

Front

What is the solution set for the inequality x > 5?

Back

The solution set for x > 5 includes all real numbers greater than 5.

Front

How do you determine if a dot is colored in when graphing an inequality?

Back

A dot is colored in (closed dot) if the inequality includes equal to (≤ or ≥) and is open if it does not (< or >).

Front

What does the inequality 5 ≥ x mean?

Back

The inequality 5 ≥ x means that x can be any number less than or equal to 5.

Front

How do you solve the inequality 2x + 3 > 7?

Back

To solve 2x + 3 > 7, subtract 3 from both sides to get 2x > 4, then divide by 2 to find x > 2.