Solving Inequalities

Front

What is an inequality?

Back

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

Front

What does the symbol '>' represent in an inequality?

Back

The symbol '>' means 'greater than' and indicates that the value on the left is larger than the value on the right.

Front

What does the symbol '<' represent in an inequality?

Back

The symbol '<' means 'less than' and indicates that the value on the left is smaller than the value on the right.

Front

What does the symbol '≥' represent in an inequality?

Back

The symbol '≥' means 'greater than or equal to' and indicates that the value on the left is either larger than or equal to the value on the right.

Front

What does the symbol '≤' represent in an inequality?

Back

The symbol '≤' means 'less than or equal to' and indicates that the value on the left is either smaller than or equal to the value on the right.

Front

How do you solve the inequality x + 5 > 7?

Back

To solve x + 5 > 7, subtract 5 from both sides to get x > 2.

Front

When graphing inequalities, what does a closed dot indicate?

Back

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

Front

When graphing inequalities, what does an open dot indicate?

Back

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

Front

How do you interpret 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 first step to solve the inequality 10.25h ≥ 550?

Back

The first step is to divide both sides by 10.25 to isolate h, resulting in h ≥ 550 / 10.25.