Exploring Equations with No Solution or Infinite Solutions

The video tutorial explains the different types of solutions that can result from solving equations: one solution, no solution, and infinitely many solutions. It provides examples for each case, demonstrating how to identify the type of solution by simplifying equations and analyzing the resulting statements. The tutorial emphasizes the importance of understanding when variables cancel out and how to interpret the truth of the remaining statement.

What are the possible types of solutions you can get when solving an equation?

• Two solutions, no solution, or infinitely many solutions

• One solution, two solutions, or infinitely many solutions

• One solution, no solution, or infinitely many solutions

• One solution, two solutions, or no solution

When solving an equation, what does it mean if you end up with a false equality statement?

• The equation has one solution

• The equation has no solution

• The equation has infinitely many solutions

• The equation has two solutions

In the example equation 10X + 30 + 8 = 18X + 30, what is the first step to solve it?

• Combine like terms

• Add 8 to both sides

• Subtract 18X from both sides

• Distribute the 10 on the left side

What is the solution to the equation 10X + 38 = 18X + 30?

• X = 0

• X = 2

• X = 1

• X = -1

What is the final step to solve the equation 10X + 38 = 18X + 30?

• Add 38 to both sides

• Subtract 30 from both sides

• Divide both sides by -8

• Multiply both sides by 8

In the equation 4(6A + 3) = 6(4A + 2), what do you get after distributing on both sides?

• 24A + 3 = 24A + 2

• 24A + 12 = 24A + 12

• 6A + 3 = 4A + 2

• 24A + 6 = 24A + 4

What does it mean if you end up with a true statement like 12 = 12 after solving an equation?

• The equation has two solutions

• The equation has one solution

• The equation has no solution

• The equation has infinitely many solutions

In the equation 12C + 36 - 30 = 12C + 36, what is the first step to solve it?

• Distribute the 12 on the left side

• Subtract 12C from both sides

• Add 36 to both sides

• Combine like terms

What is the result of combining like terms in the equation 12C + 36 - 30?

• 12C + 36

• 12C - 6

• 12C + 66

• 12C + 6

What does it mean if you end up with a false statement like 6 = 36 after solving an equation?

• The equation has two solutions

• The equation has one solution

• The equation has no solution

• The equation has infinitely many solutions