Understanding Linear and Compound Inequalities

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

• Multiply both sides by a positive number

• Reverse the inequality symbol

• Add a constant to both sides

• Switch the variable to the other side

How is the solution to a linear inequality represented graphically?

• As a single point on the number line

• As a shaded region on the number line

• As a vertical line on a graph

• As a horizontal line on a graph

When solving linear inequalities, what should you do if you distribute a positive number?

• Subtract the number from both sides

• Switch the inequality symbol

• Add the number to both sides

• Keep the inequality symbol the same

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

• 'Or' requires both conditions to be true, 'and' requires only one

• 'Or' requires only one condition to be true, 'and' requires both

• 'Or' uses multiplication, 'and' uses division

• 'Or' is solved by adding inequalities, 'and' by subtracting

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

• Numbers that satisfy at least one inequality

• Numbers that are equal to zero

• Numbers that satisfy neither inequality

• Numbers that satisfy both inequalities

How do you graphically represent an 'or' compound inequality?

• Shade only one side of the number line

• Do not shade any region

• Shade the regions outside the two points

• Shade the region between the two points

What is the main characteristic of an 'and' compound inequality?

• It involves only positive numbers

• It requires both conditions to be true

• It requires only one condition to be true

• It involves only negative numbers

In a three-sided inequality, what is the goal?

• To isolate the variable in the middle

• To add all sides together

• To isolate the variable on one side

• To eliminate the variable

How is the solution to an 'and' compound inequality represented on a number line?

• As a vertical line

• As two separate shaded regions

• As a shaded region between two points

• As a single point

What does the interval notation for an 'and' compound inequality look like?

• An interval starting from zero

• A single interval between two numbers

• Two separate intervals

• An interval ending at infinity