Understanding Linear Inequalities

What does the symbol '>' represent in inequalities?

• Less than

• Greater than

• Not equal to

• Equal to

When graphing the solution of an inequality on a number line, what does an open dot signify?

• The inequality is an 'and' inequality

• The number is included in the solution

• The inequality is an 'or' inequality

• The number is not included in the solution

What does a closed dot on a number line indicate when graphing an inequality?

• The inequality is strict

• The number is part of the solution

• The inequality is non-strict

• The number is not part of the solution

What is the purpose of using a number line when solving inequalities?

• To simplify the inequality

• To find the exact solution

• To visually represent the solution set

• To check for errors in calculations

What must you remember to do when dividing both sides of an inequality by a negative number?

• Add the same number to both sides

• Multiply both sides by a positive number

• Subtract the same number from both sides

• Flip the inequality sign

How can you determine the direction of shading on a number line for an inequality?

• By the coefficient of the variable

• By the position of the variable

• By the constant term

• By the type of inequality

In an 'or' inequality, what does the solution set represent?

• Values that satisfy at least one of the inequalities

• Values that satisfy both inequalities simultaneously

• Values that do not satisfy either inequality

• Values that are less than zero

In the context of inequalities, what does the term 'compound inequality' refer to?

• An inequality with a single variable

• An inequality with multiple variables

• Two or more inequalities combined

• An inequality with no solution

How are 'and' inequalities typically represented on a number line?

• With arrows pointing in opposite directions

• With no shaded region

• With a single shaded region between two points

• With two separate shaded regions

What is the main difference between 'and' and 'or' inequalities?

• 'Or' inequalities require both conditions to be true

• 'And' inequalities require both conditions to be true

• 'Or' inequalities have solutions that overlap

• 'And' inequalities have solutions that overlap