Solving Equations with Variables on Both Sides

Why do we move variables to one side in an equation?

• To isolate the variable and solve the equation

• To make the equation look simpler

• Because it's a rule with no real purpose

• To ensure the equation remains balanced

What is the first step in checking if your solution is correct?

• Multiply the solution by each coefficient

• Add the solution to each side of the equation

• Substitute the solution back into the original equation

• Divide the solution by the coefficient of the variable

What does a positive result when checking your solution indicate?

• The solution is definitely correct

• The solution needs to be re-evaluated

• The solution is possibly correct

• The solution is incorrect

In the second example, why does it not matter which side you choose for the variables?

• Because there are an equal number of terms on both sides

• Because all terms are positive

• Because the equation is symmetrical

• Because there are only two terms

What is the purpose of the distributive property in solving equations?

• To combine like terms

• To isolate the variable

• To eliminate parentheses

• To balance both sides of the equation

How do you solve an equation after distributing and collecting like terms?

• By performing the inverse operation on both sides

• By adding or subtracting terms to both sides

• By dividing both sides by the leading coefficient

• By multiplying both sides by the leading coefficient

What does it mean to perform 'inverse operations' in the context of solving equations?

• Performing the opposite operation on both sides to maintain balance

• Performing the opposite operation on one side

• Performing the same operation on both sides

• Ignoring the operations and focusing on the result

Why is it important to check your solution after solving an equation?

• To verify the solution satisfies the original equation

• To ensure the equation remains balanced

• Because it's a mandatory step in all math problems

• To find alternative solutions

What role do parentheses play in equations with variables on both sides?

• They separate the variables from the constants

• They indicate multiplication

• They group terms that need to be distributed

• They are used to add complexity to the problem

After distributing and collecting like terms, what is the next step?

• Divide each term by the variable's coefficient

• Isolate the variable by performing inverse operations

• Combine all constants on one side

• Multiply each term by the variable's coefficient