Solving Complicated Linear Equations

The video tutorial explains how to solve linear equations with additional terms and negative numbers. It begins with a simple equation, 3x + 5 = 17, and demonstrates a visual method to understand the process. The tutorial then provides a step-by-step solution, emphasizing the importance of maintaining equality by performing the same operations on both sides. The video concludes with a more complex example, 7x - 2 = -10, involving negative numbers, reinforcing the same principles.

What operation do we perform first to simplify the equation 3x + 5 = 17?

• Add 5 to both sides

• Subtract 5 from both sides

• Multiply both sides by 3

• Divide both sides by 3

After subtracting 5 from both sides of the equation 3x + 5 = 17, what is the new equation?

• 3x - 5 = 17

• x = 12

• 3x + 5 = 12

• 3x = 12

What is the value of x in the equation 3x = 12?

• 4

• 15

• 3

• 9

What does subtracting 5 from both sides of an equation symbolically represent?

• Dividing each side by 5

• Multiplying each side by 5

• Removing 5 objects from each side

• Adding 5 objects to one side

What is the result of dividing both sides of the equation 3x = 12 by 3?

• x = 3

• x = 4

• x = 36

• x = 12

In the equation 7x - 2 = -10, what operation do we perform to isolate the term 7x?

• Divide both sides by 7

• Add 2 to both sides

• Subtract 2 from both sides

• Multiply both sides by 7

What is the new equation after adding 2 to both sides of 7x - 2 = -10?

• 7x = -12

• 7x = -8

• x = -8

• 7x + 2 = -8

What does adding 2 to both sides of the equation 7x - 2 = -10 achieve?

• It doubles the coefficient of x

• It eliminates the constant term

• It halves the coefficient of x

• It isolates the variable x

How do we find the value of x in the equation 7x = -8?

• Subtract 7 from both sides

• Multiply both sides by 7

• Add 7 to both sides

• Divide both sides by 7

What is the value of x in the equation 7x = -8?

• 8/7

• -1 and 1/7

• -8/7

• 1 and 1/7