Exploring Multi-Step Inequalities

The video tutorial covers solving multi-step inequalities, including graphing and writing interval notations. It explains the importance of flipping the inequality sign when multiplying or dividing by a negative number. The tutorial provides several examples, demonstrating how to solve inequalities, graph them, and write the solutions in interval notation. Key concepts such as open and closed circles, parentheses, and brackets are discussed, along with practical examples involving distribution and combining like terms.

What should you do to the inequality sign when you multiply or divide by a negative number?

• Subtract 1 from it

• Leave it unchanged

• Flip it

• Add 1 to it

What do parentheses in interval notation indicate?

• The value is included

• The value is excluded

• The value is zero

• The value is negative

In interval notation, what symbol is always used with infinity?

• Parenthesis

• Bracket

• Comma

• Colon

What is the solution to the inequality 2x - 8 > 12?

• x < -10

• x > -10

• x < 10

• x > 10

How do you graph the solution x > 10 on a number line?

• Closed circle at 10, shade to the left

• Open circle at 10, shade to the left

• Open circle at 10, shade to the right

• Closed circle at 10, shade to the right

What is the interval notation for the solution x > 10?

• [10, ∞)

• (10, ∞)

• (-∞, 10]

• (-∞, 10)

When solving -3x + 20 ≥ 26, what is the first step?

• Add 20 to both sides

• Multiply both sides by -3

• Divide both sides by -3

• Subtract 20 from both sides

What is the solution to the inequality -3x ≥ 6?

• x ≤ 2

• x ≥ -2

• x ≤ -2

• x ≥ 2

How do you graph the solution x ≤ -2 on a number line?

• Closed circle at -2, shade to the right

• Open circle at -2, shade to the right

• Closed circle at -2, shade to the left

• Open circle at -2, shade to the left

What is the interval notation for the solution x ≤ -2?

• [2, ∞)

• (-∞, -2]

• (2, ∞)

• (-∞, -2)