Exploring Solutions in Mathematical Equations

The video tutorial explains how to determine equations with one solution, infinitely many solutions, and no solutions. It begins with a brief overview of each type of solution, followed by detailed examples. For one solution, the equation results in a single value for the variable. Infinitely many solutions occur when both sides of the equation are identical, allowing any value for the variable. No solutions arise when the equation simplifies to a false statement, such as two unequal numbers. The tutorial provides step-by-step examples for each case, ensuring a clear understanding of the concepts.

What are the three types of solutions an equation can have?

• One solution, two solutions, and no solutions

• One solution, infinitely many solutions, and no solutions

• Two solutions, infinitely many solutions, and no solutions

• One solution, two solutions, and infinitely many solutions

Which of the following represents an equation with one solution?

• x = x

• x = 10

• 2x + 9 = 2x + 9

• 4 = 0

What does it mean if an equation has infinitely many solutions?

• The equation is valid for any value of the variable.

• The equation has two solutions.

• The equation has no valid solutions.

• The equation has exactly one solution.

Which of the following equations has no solutions?

• x = x

• x = 5

• 4 = 0

• 2x + 9 = 2x + 9

In the example of an equation with one solution, what is the final value of x?

• 3

• 2

• 5

• 4

What is the first step in solving the equation 2x + 4 = 10?

• Multiply both sides by 2

• Subtract 4 from both sides

• Add 4 to both sides

• Divide both sides by 2

In the example of an equation with infinitely many solutions, what is the result after distributing on the left side?

• 2x + 4

• 2x - 4

• 2x + 2

• 2x - 2

What does it mean if both sides of an equation are identical?

• The equation has one solution.

• The equation has no solutions.

• The equation has two solutions.

• The equation has infinitely many solutions.

In the example of an equation with no solutions, what is the final comparison that shows there are no solutions?

• Negative four equals negative two

• 2x = 2x

• 2x - 4 = 2x - 2

• 4 = 0

What is the first step in solving the equation 2x - 4 = 2(x - 1)?

• Subtract 4 from both sides

• Divide both sides by 2

• Add 4 to both sides

• Distribute the 2 on the right side