Solve Inequalities: Key Concepts and Techniques

What is the main difference between solving equations and solving inequalities?

• Equations are harder to solve.

• Inequalities have more than one solution.

• Equations use different symbols.

• Inequalities are always positive.

Which symbol represents 'greater than or equal to'?

• ≤

• ≥

• >

• <

When solving the inequality 2x - 1 + 1 > 7, what is the first step?

• Combine like terms.

• Use the distributive property.

• Subtract 1 from both sides.

• Divide by 2.

How do you check if your solution to an inequality is correct?

• Ask a friend.

• Plug in any number.

• Plug in a number within the solution range.

• Use a calculator.

What type of circle is used on a number line for 'greater than' or 'less than' inequalities?

• Dotted circle

• Shaded circle

• Open circle

• Closed circle

What must you do when you multiply or divide both sides of an inequality by a negative number?

• Subtract the same number from both sides.

• Flip the inequality symbol.

• Keep the inequality symbol the same.

• Add the same number to both sides.

In the inequality -3x - 3 > 9, what is the result after dividing both sides by -3?

• x < -4

• x > -4

• x < 4

• x > 4

What is the inequality to determine the number of sets of glasses Evelyn needs to buy if each set contains 12 glasses and she needs at least 769 glasses?

• 12x + 205 ≥ 769

• 12x + 205 ≤ 769

• 12x - 205 ≥ 769

• 12x - 205 ≤ 769

If Evelyn currently has 205 glasses and each set contains 12 glasses, how many sets does she need to buy to have at least 769 glasses?

• 45

• 46

• 47

• 48

What is the correct inequality for a shipping container problem if the answer is less than or equal to 135?

• x < 135

• x ≥ 135

• x > 135

• x ≤ 135