Understanding Linear Inequalities

The video tutorial explains how to solve a linear inequality in one variable. It covers the process of solving the inequality, expressing the solution using inequality notation, graphing the solution, and using interval notation. Key steps include distributing terms, combining like terms, and dividing by a positive number without reversing the inequality symbol. The tutorial also demonstrates graphing the solution on a number line and using interval notation to express the solution.

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

• Add a positive number to both sides

• Reverse the inequality symbol

• Subtract a negative number from both sides

• Keep the inequality symbol the same

What is the first step in solving the inequality 36x ≤ 4(-7x + 32)?

• Add 7x to both sides

• Distribute the 4 on the right side

• Subtract 32 from both sides

• Divide both sides by 4

After distributing and combining like terms, what is the resulting inequality before the final step?

• 64x ≤ 128

• 36x ≤ 128

• 36x ≥ 128

• 64x ≥ 128

When solving the inequality 64x ≤ 128, what is the value of x?

• x ≥ 2

• x ≥ 1

• x ≤ 2

• x ≤ 1

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

• Open point at 2 and line to the left

• Closed point at 2 and line to the left

• Open point at 2 and line to the right

• Closed point at 2 and line to the right

Which tool is used to plot a closed point on a graph?

• Bracket tool

• Arrow tool

• Dot tool

• Line segment tool

What type of bracket is used in interval notation to indicate that an endpoint is included?

• Curly bracket

• Square bracket

• Angle bracket

• Rounded parenthesis

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

• Square bracket

• Angle bracket

• Rounded parenthesis

• Curly bracket

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

• [2, ∞)

• [2, -∞)

• (-∞, 2]

• (-∞, 2)

What is the purpose of using the preview button in the homework system?

• To see how the system interprets entries

• To submit the homework

• To save the work

• To check for spelling errors