Solving Equations with Variables on Both Sides

The video tutorial covers solving equations with variables on both sides. It begins with an introduction to simplifying equations and provides three examples demonstrating different methods of solving. The tutorial also discusses special cases where equations have no solution or all real numbers as solutions, emphasizing the importance of understanding coefficients and constants.

What is the first step in solving equations with variables on both sides?

• Multiply both sides by the same number

• Add the same number to both sides

• Simplify both sides of the equation

• Move all constants to one side

In the first example, what is the result after subtracting 5 from both sides of the equation 2x + 5 = 4x - 13?

• 2x = 4x - 5

• 2x = 4x - 8

• 2x = 4x - 18

• 2x = 4x - 13

What is the final value of x in the first example?

• x = 9

• x = 6

• x = -6

• x = -9

In the second example, what operation is performed first?

• Combining like terms

• Subtracting variables

• Distributing

• Adding constants

What is the final value of x in the second example?

• x = -5

• x = 5

• x = 3

• x = -3

In the third example, what is the result after combining like terms on the left side?

• 6x + 13

• 6x - 8

• 6x + 8

• 6x + 21

What is the final value of x in the third example?

• x = 3

• x = 1

• x = 4

• x = 2

What does it mean if you end up with a statement like 24 = 24 when solving an equation?

• The solution is x = 0

• All real numbers are solutions

• The solution is x = 24

• There is no solution

What does it mean if you end up with a statement like 24 = 36 when solving an equation?

• The solution is x = 24

• There is no solution

• The solution is x = 36

• All real numbers are solutions

In the special case where variables cancel out and you get 0 = 7, what is the conclusion?

• All real numbers are solutions

• x = 7

• x = 0

• No solution