Determining Solutions in Equations

This video tutorial by Mr. Weaver covers 8th grade module three, lesson five, focusing on determining the number of solutions in linear equations. It explains how to identify equations with no solutions, one solution, or infinitely many solutions by simplifying and comparing coefficients and constants. The tutorial includes examples and exercises to help students understand and apply these concepts.

What does it mean if an equation has no solution?

• There is exactly one value that makes the equation true.

• Any value of the variable will make the equation true.

• No value of the variable will make the equation true.

• The equation cannot be simplified.

Which of the following is an example of an equation with one solution?

• 4x - 4 = 4x - 4

• x + 2 = 5

• 2x + 5 = 2x + 5

• 3x + 4 = 3x

In the example of solving 6(x - 3) + 10 = 2(3x - 4), what is the final simplified form before determining the number of solutions?

• 6x - 18 + 10 = 6x - 8 + 10

• 6x - 18 = 6x - 8

• 6x - 8 = 6x - 8

• 6x - 18 + 10 = 6x - 8

What does it indicate if, after simplifying an equation, you get a true statement like -8 = -8?

• The equation has no solution.

• The equation has one solution.

• The equation has infinitely many solutions.

• The equation is invalid.

In the example of solving 8(4 - 2x) = 4(3 - 5x) + 4x, what is the final simplified form before determining the number of solutions?

• 32 - 16x = 12 - 12x

• 32 - 16x = 12 - 20x

• 32 - 16x = 12 - 4x

• 32 - 16x = 12 - 16x

What does it indicate if, after simplifying an equation, you get a false statement like 32 = 12?

• The equation has no solution.

• The equation has one solution.

• The equation has infinitely many solutions.

• The equation is invalid.

How can you identify an equation with no solution by looking at the coefficients and constants?

• Different coefficients and different constants.

• Same coefficients and different constants.

• Same coefficients and same constants.

• Different coefficients and same constants.

How can you identify an equation with infinitely many solutions by looking at the coefficients and constants?

• Same coefficients and different constants.

• Same coefficients and same constants.

• Different coefficients and same constants.

• Different coefficients and different constants.

What must be true for an equation to have one solution?

• The equation must be linear.

• The coefficients must be the same.

• The constants must be the same.

• The coefficients must be different.

To create an equation with no solution, what should you ensure about the coefficients and constants?

• Same coefficients and different constants.

• Different coefficients and different constants.

• Same coefficients and same constants.

• Different coefficients and same constants.