Understanding Linear Inequalities and Notation

This video tutorial is designed for M-104 classes and focuses on solving linear inequalities in one variable, particularly those involving fractions. The instructor explains the process of finding the least common denominator to eliminate fractions, solving the inequality, and graphing the solution on a number line. The video concludes with a demonstration of writing the solution in interval notation.

What is the main focus of this video tutorial?

• Understanding complex numbers

• Solving quadratic equations

• Solving linear inequalities with fractions

• Graphing linear equations

Why is it important to eliminate fractions when solving inequalities?

• It changes the solution

• It simplifies the problem

• It is not necessary

• It makes the problem more complex

What is the first step in eliminating fractions from an inequality?

• Adding fractions

• Multiplying fractions

• Subtracting fractions

• Finding the least common denominator

What is the least common denominator for the fractions with denominators 6 and 12?

• 6

• 12

• 24

• 18

What is the purpose of multiplying through by the least common denominator?

• To increase the number of fractions

• To eliminate fractions

• To change the inequality sign

• To add more variables

After multiplying by the LCD, what should be the next step?

• Divide by zero

• Change the inequality to an equation

• Combine like terms

• Add more fractions

What is the result of combining like terms in the inequality 8x + 18 ≥ 2x - 1?

• 4x ≥ 5

• 10x ≥ 17

• 6x ≥ -19

• 8x ≥ 2

How do you convert the solution x ≥ -19/6 to a mixed number?

• x ≥ -2 1/3

• x ≥ -3 2/3

• x ≥ -3 1/6

• x ≥ -4 1/6

On a number line, how is the point -3 1/6 represented?

• With a triangle

• With a square bracket

• With a closed circle

• With an open circle

What does the square bracket indicate on a number line?

• The point is a midpoint

• The point is an estimate

• The point is not included

• The point is included