Solving Linear Inequalities in One Variable

This video tutorial covers solving linear inequalities in one variable. It explains the difference between linear equations and inequalities, highlighting that inequalities have multiple solutions. The tutorial demonstrates how to express solutions using inequalities, graphs, and interval notation. It provides examples of solving inequalities, emphasizing the need to reverse the inequality symbol when multiplying or dividing by a negative number. The video also shows how to use graphing calculators to find solutions graphically.

What symbol differentiates a linear inequality from a linear equation?

• Equal sign

• Multiplication sign

• Plus sign

• Greater than symbol

How can solutions to linear inequalities be represented?

• Using a single number

• Using quadratic equations

• Using inequalities, graphs, or interval notation

• Using matrices

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

• Square both sides

• Reverse the inequality symbol

• Do nothing

• Add 1 to both sides

What is the correct graph representation for 'x > -3'?

• Closed circle on -3, arrow to the right

• Closed circle on -3, arrow to the left

• Open circle on -3, arrow to the left

• Open circle on -3, arrow to the right

In interval notation, how is infinity always represented?

• With an angle bracket

• With a square bracket

• With a curly bracket

• With a rounded parenthesis

What does a closed circle on a graph indicate?

• The number is included in the solution

• The solution is negative

• The solution is positive

• The number is not included in the solution

What does an open circle on a graph signify?

• The solution is infinite

• The number is included in the solution

• The number is not included in the solution

• The solution is zero

How is 'x is less than 9 1/3' represented in interval notation?

• (-∞, 9 1/3]

• (-∞, 9 1/3)

• [9 1/3, ∞)

• [9 1/3, ∞]

When graphing 'y1 < y2' on a graphing calculator, what are you looking for?

• Where y1 is above y2

• Where y1 and y2 are parallel

• Where y1 intersects y2

• Where y1 is below y2

What is the solution set for 'x ≤ 2' using a graphing calculator?

• x ≥ 2

• x < 2

• x ≤ 2

• x > 2