Determining Solutions to One-Variable Equations

This video tutorial for 8th graders covers Lesson 11, Session 2, focusing on determining the number of solutions to one-variable equations. The teacher introduces a problem involving sloths and guides students through solving an equation step-by-step. The lesson emphasizes understanding when equations have no solutions and provides practice problems to reinforce learning.

What is the main topic of Lesson 11 Session 2?

• Determining the number of solutions to one-variable equations

• Learning about zoology

• Understanding fractions

• Studying the heights of trees

In the problem involving the sloths, what does the variable 'x' represent?

• The distance between the sloths

• The number of sloths

• The height of the tree

• The time in minutes

What is the first step in solving the equation 1/2(2x + 4) = x + 3?

• Multiplying both sides by 2

• Adding 4 to both sides

• Distributing the 1/2 into the parentheses

• Subtracting 2 from both sides

After distributing the 1/2, what is the simplified form of the equation?

• x + 2 = x + 3

• 2x + 4 = x + 3

• x + 4 = x + 3

• x + 2 = 3

What conclusion is reached when the equation simplifies to 0 = 1?

• The equation has one solution

• The equation is incorrect

• The equation has no solution

• The equation has infinitely many solutions

Why does the equation 2x + 4 = x + 3 have no solution?

• Because it is not a valid equation

• Because it has infinitely many solutions

• Because the variables cancel out and leave a false statement

• Because 2 equals 3

What does it mean if an equation simplifies to 0 = 0?

• The equation has no solution

• The equation has one solution

• The equation has infinitely many solutions

• The equation is incorrect

In the practice problem, what is the solution to the equation 9(-1 + x) + 1 = 12x + 1?

• No solution

• x = -3

• x = 3

• x = 0

Which of the following equations has no solution?

• 9(-1 + x) + 1 = 12x + 1

• x - 7 = x - 7

• 0.5y = 0

• x + 2 = x + 3

What does the final practice problem involving Aaron and Santo demonstrate?

• That they started at the same point

• That they have the same speed

• That they are at different distances from the start of the trail

• That they are at the same distance from the start of the trail