Understanding and Solving Linear Inequalities

The video tutorial explains how to solve and graph linear inequalities, emphasizing the importance of reversing the inequality symbol when multiplying or dividing by a negative number. It provides two examples, demonstrating the process of isolating the variable, solving the inequality, and expressing the solution using interval notation. The tutorial also covers graphing the solutions on a number line, highlighting the use of open and closed points to indicate whether endpoints are included in the interval.

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

• Leave it unchanged

• Reverse it

• Add a negative sign

• Multiply by zero

In the first example, what operation is performed first to isolate the variable?

• Multiplication

• Division

• Addition

• Subtraction

What is the solution to the first example inequality expressed in interval notation?

• (-∞, 4)

• (-∞, -4]

• (-4, ∞)

• [-4, ∞)

How is the solution to the first example inequality represented on a graph?

• A closed point on -4 with an arrow to the right

• An open point on -4 with an arrow to the right

• A closed point on -4 with an arrow to the left

• An open point on -4 with an arrow to the left

What does an open point on a graph indicate about the number it represents?

• The number is a boundary and included

• The number is an approximation

• The number is not included in the interval

• The number is included in the interval

In the second example, what is the first step to isolate the variable?

• Add 2 to both sides

• Subtract 2 from both sides

• Divide by 7

• Multiply by 7

What is the solution to the second example inequality expressed as an inequality?

• X > 1

• X ≥ 1

• X < 1

• X ≤ 1

How is the solution to the second example inequality represented on a graph?

• An open point on 1 with an arrow to the right

• A closed point on 1 with an arrow to the right

• An open point on 1 with an arrow to the left

• A closed point on 1 with an arrow to the left

What is the interval notation for the solution to the second example inequality?

• (-∞, 1]

• (-∞, 1)

• [1, ∞)

• (1, ∞)

What does a closed point on a graph indicate about the number it represents?

• The number is included in the interval

• The number is a boundary but not included

• The number is not included in the interval

• The number is an approximation