Understanding Linear Inequalities

The video tutorial explains how to solve a linear inequality, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It demonstrates solving the inequality step-by-step, graphing the solution on a number line, and expressing the solution using interval notation. The tutorial also highlights the use of open and closed points, parentheses, and square brackets in graphing and interval notation.

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

• Reverse the inequality symbol

• Add a positive number to both sides

• Subtract a negative number from both sides

• Keep the inequality symbol the same

What is the first step in solving the inequality -5x + 4x < 1?

• Add 4x to both sides

• Subtract 4x from both sides

• Multiply both sides by -1

• Divide both sides by 4

After combining like terms, what is the next step to isolate the variable x in the inequality x - 12 < 1?

• Divide both sides by 12

• Multiply both sides by 12

• Add 12 to both sides

• Subtract 12 from both sides

When solving the inequality -x < 1, what operation is necessary to solve for x?

• Divide both sides by -1

• Subtract 1 from both sides

• Add 1 to both sides

• Multiply both sides by 1

What is the solution to the inequality -x < 1 after reversing the inequality symbol?

• x = 1

• x > 1

• x ≤ 1

• x < 1

How is an open point used on a number line when graphing the solution x > 1?

• To show that the solution is equal to 1

• To indicate that 1 is included in the solution

• To show that the solution is less than 1

• To indicate that 1 is not included in the solution

What symbol is used to indicate that an endpoint is not included in interval notation?

• Square bracket

• Curly brace

• Open parenthesis

• Closed parenthesis

In interval notation, how is the interval x > 1 expressed?

• (1, ∞]

• [1, ∞]

• [1, ∞)

• (1, ∞)

What symbol is always used with infinity in interval notation?

• Square bracket

• Open parenthesis

• Curly brace

• Closed parenthesis

How can you access the infinity symbol on a keyboard?

• Using the letter I

• Using the number 8

• Using two lowercase o's

• Using the letter O