Solving Linear Inequalities: Key Concepts and Techniques

What symbols are used to represent inequalities?

• None of the above

• Equal to, not equal to

• Less than, greater than, less than or equal to, greater than or equal to

• Plus, minus, multiply, divide

What does the addition property of inequalities state?

• Multiplying both sides by a positive number reverses the inequality

• Adding the same number to both sides of an inequality does not change the inequality

• None of the above

• Subtracting the same number from both sides of an inequality reverses the inequality

What happens when you multiply both sides of an inequality by a negative number?

• The inequality reverses direction

• The inequality is invalid

• The inequality becomes an equation

• The inequality remains the same

What is a compound inequality?

• None of the above

• An inequality with a single condition

• An inequality with two conditions

• An inequality with no conditions

How do you solve a compound inequality with 'and'?

• None of the above

• Solve only one of the inequalities

• Solve each inequality separately and find the intersection of the solutions

• Solve each inequality separately and find the union of the solutions

What is the first step in solving the inequality 30 + 15R + 7 ≥ 127?

• Subtract 7 from both sides

• Combine like terms on the left side

• Multiply by the distributive property

• Divide by 15

What is the interval notation for the solution R ≥ 6?

• (6, ∞)

• [6, ∞]

• [6, ∞)

• (6, ∞]

When solving the inequality 28 - 7X < 28X + 28, what is the next step after distributing?

• Subtract 28X from both sides

• Add 28 to both sides

• Divide by -7

• Add 7X to both sides

What is the interval notation for the solution X > 0?

• [0, ∞]

• [0, ∞)

• (0, ∞]

• (0, ∞)

What does the interval notation [-6/5, 2) represent?

• All numbers between -6/5 and 2, excluding -6/5 but including 2

• All numbers between -6/5 and 2, excluding both -6/5 and 2

• All numbers between -6/5 and 2, including both -6/5 and 2

• All numbers between -6/5 and 2, including -6/5 but not 2