Solving Equations with Variables on Both Sides

What is the primary goal when solving equations with variables on both sides?

• To make all coefficients positive

• To ensure the equation remains balanced

• To get the variable on one side

• To eliminate all variables

What is the correct approach when you have variables on both sides of an equation?

• Divide both sides by the variable

• Multiply both sides by the variable

• Isolate the variable on one side by adding or subtracting

• Always move the variables to the right side

Why do we prefer to subtract the smaller variable term from both sides of an equation?

• To simplify the calculation process

• Because it's the official rule

• To avoid getting a negative coefficient

• To make the equation more complex

What should you do if you end up with a negative coefficient for the variable?

• It's okay to proceed and solve

• Multiply both sides by -1

• The equation is unsolvable

• Start over with the equation

What is the benefit of having a positive coefficient for the variable when solving an equation?

• It makes the equation true

• It simplifies the solving process

• It ensures a unique solution

• It guarantees the solution will be positive

When given the choice, why is it better to subtract 3x from both sides instead of 17x?

• To make the equation shorter

• Because 3 is a prime number

• To avoid negative numbers

• It results in a simpler equation

What is the result of adding 6x to both sides of an equation with a -6x term?

• It cancels out the -6x

• It makes the equation unsolvable

• It doubles the -6x term

• It has no effect on the equation

What is the final step in solving the equation 11x = 12?

• Subtract 11 from both sides

• Divide both sides by 11

• Add 11 to both sides

• Multiply both sides by 11

Why is it important to check your solution by plugging it back into the original equation?

• To ensure the solution is positive

• To find alternative solutions

• To verify the solution is correct

• Because it's a mandatory step

What does solving the equation 4n = 21 - 4 result in?

• n = 1

• n = 17/4

• n = 5

• n = 4