Solving Equations with Variables on Both Sides

The video tutorial teaches how to solve equations with the same variable on both sides of the equal sign. It emphasizes not combining like terms across the equal sign and provides a step-by-step guide to simplifying and solving equations. The tutorial includes example problems, checks for solutions, and offers advanced problem-solving techniques.

Why can't you combine like terms across an equal sign?

• It's considered a mathematical error

• It simplifies the equation too much

• It's only allowed in expressions, not equations

• It makes the equation unsolvable

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

• Combine like terms

• Find the side with the least amount of the variable and eliminate it from that side

• Divide both sides by the variable

• Multiply both sides by the variable

How do you eliminate a variable from one side of an equation?

• By adding the variable to both sides

• By subtracting the variable from both sides

• By dividing both sides by the variable

• By performing the opposite operation of the variable's coefficient

What does it mean to do the opposite operation when solving an equation?

• To reverse the last step you took

• To perform the inverse mathematical operation to both sides

• To ignore the operation and solve visually

• To perform the same operation on both sides

What happens when you subtract the same variable term from both sides of an equation?

• The variable term becomes zero

• The variable gets eliminated from the equation

• The equation becomes simpler

• Both A and C

What is the purpose of checking your solution in an equation?

• To ensure the equation is balanced

• To verify the solution is correct by substituting it back into the original equation

• To find alternative solutions

• To simplify the equation further

What should you do if one side of the equation only has variables and the other side has a constant?

• Get all the variables to the side that only has variables

• Add the constant to both sides

• Eliminate the variable from the side with the constant

• Multiply both sides by the constant

What is a common mistake students make when solving equations with variables on both sides?

• Combining like terms across the equal sign

• Forgetting to perform operations on both sides

• Stopping the process too early and leaving an expression instead of an equation

• Checking their solution incorrectly

How can you verify that your solution to an equation is correct?

• By solving the equation again

• By checking if the equation is balanced

• By asking someone else to solve it

• By substituting the solution back into the original equation

Why is it important to practice solving equations with variables on both sides?

• To be able to solve them faster

• All of the above

• To memorize the equations

• To improve mathematical intuition