Solving Multi-Step Equations with Variables on Both Sides

This video tutorial by Mr. J introduces solving equations with variables on both sides. It explains the process of isolating the variable on one side of the equation using inverse operations. Two examples are provided: one solving for x and another for y, demonstrating the step-by-step approach to reach the solution. The video concludes with a summary of the key steps involved in solving such equations.

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

• Multiply both sides by the variable

• Isolate the variable on one side

• Subtract the variable from one side

• Divide both sides by the variable

Why is it suggested to avoid negatives when isolating variables?

• To simplify calculations

• To ensure the variable is on the left side

• To make the equation more complex

• To avoid division by zero

In the equation 5x - 4 = 2x + 11, what operation is performed first to isolate the variable?

• Divide both sides by 5

• Subtract 2x from both sides

• Add 4 to both sides

• Multiply both sides by 2

After isolating the variable on one side, what is the next step in solving the equation?

• Subtract the constants

• Multiply by the variable's coefficient

• Add the constants

• Divide by the variable's coefficient

What is the solution to the equation 5x - 4 = 2x + 11?

• x = 5

• x = 6

• x = 3

• x = 4

What is the purpose of using inverse operations in solving equations?

• To subtract coefficients

• To cancel out terms

• To multiply variables

• To add constants

How do we verify the solution of an equation with variables on both sides?

• Divide the equation by the solution

• Multiply the solution by the coefficient

• Substitute the solution back into the original equation

• Add the solution to both sides of the equation

In the equation 3y + 8 = 10y - 6, what is the first step to solve for y?

• Add 6 to both sides

• Subtract 3y from both sides

• Divide both sides by 3

• Multiply both sides by 10

What is the final step in solving the equation 3y + 8 = 10y - 6 for y?

• Divide both sides by 7

• Subtract 6 from both sides

• Multiply both sides by 7

• Add 8 to both sides

What is the solution to the equation 3y + 8 = 10y - 6?

• y = 4

• y = 3

• y = 2

• y = 1