Solving and Graphing Inequalities Review for Flashcard

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

How do you solve a linear inequality?

Back

To solve a linear inequality, isolate the variable on one side of the inequality sign using inverse operations, similar to solving an equation, while remembering to reverse the inequality sign if you multiply or divide by a negative number.

Front

What does the symbol '>' represent in inequalities?

Back

'>' means 'greater than'. It indicates that the value on the left side of the inequality is larger than the value on the right side.

Front

What does the symbol '<' represent in inequalities?

Back

'<'' means 'less than'. It indicates that the value on the left side of the inequality is smaller than the value on the right side.

Front

What does the symbol '≥' represent in inequalities?

Back

'≥' means 'greater than or equal to'. It indicates that the value on the left side is either greater than or equal to the value on the right side.

Front

What does the symbol '≤' represent in inequalities?

Back

'≤' means 'less than or equal to'. It indicates that the value on the left side is either less than or equal to the value on the right side.

Front

How do you graph a linear inequality on a number line?

Back

To graph a linear inequality on a number line, first draw a number line, then use an open circle for '>' or '<' and a closed circle for '≥' or '≤'. Shade the region that represents the solution set.

Front

What is the solution set of an inequality?

Back

The solution set of an inequality is the set of all values that satisfy the inequality. It can be represented on a number line or in interval notation.

Front

What is the difference between 'and' and 'or' in compound inequalities?

Back

'And' means both conditions must be true (intersection), while 'or' means at least one condition must be true (union).

Front

How do you solve compound inequalities?

Back

To solve compound inequalities, solve each inequality separately and then combine the results according to whether 'and' or 'or' is used.