Solving Linear Equations and Applications

The video tutorial covers solving linear equations in both standard and non-standard forms, using examples from a textbook. It explains how to handle equations with fractions, combine like terms, and identify scenarios with no solutions or infinite solutions. The tutorial also includes real-world applications, such as calculating concert ticket sales revenue and determining gross pay from an annual salary with bonuses.

What is the first step in solving a linear equation in standard form?

• Eliminate fractions

• Combine like terms

• Distribute terms

• Isolate the variable

In Example A, what operation is used to eliminate the fraction?

• Division

• Multiplication

• Subtraction

• Addition

What is the result of solving the equation x/3 + 3 = 0?

• x = 3

• x = -9

• x = 9

• x = 0

In Example B, what is the first step to solve 3y + 8 - 5y = 4?

• Distribute terms

• Combine like terms

• Move terms across the equation

• Eliminate fractions

What is the value of y in the equation 3y + 8 - 5y = 4?

• y = -4

• y = 4

• y = 2

• y = -2

In Example C, what indicates that the equation has no solution?

• The equation results in zero

• The equation results in a false statement

• The variable cancels out

• Both sides are equal

What is the result of solving the equation 2x + 3 = 2(x + 4)?

• Infinite solutions

• No solution

• x = 4

• x = 3

In Example D, what indicates that the equation has infinite solutions?

• The equation results in a true statement

• The equation results in zero

• The variable cancels out

• Both sides are equal

What is the result of solving the equation 4(x + 3) = 4x + 12?

• x = 3

• x = 4

• No solution

• Infinite solutions

In the ticket sales problem, what is the cost of each stadium seat?

• $175

• $95

• $100

• $250