Intro to Equations with Variables on Both Sides

CLT often can mean

• Combine Like Terms

• Constant Linear Terms

• Collect Like Terms

• Common Linear Terms

What is the primary difference between "combining like terms" and "collecting like terms" in the context of solving equations?

• Combining like terms happens on one side of the equation, while collecting like terms involves moving terms across the equals sign.

• Combining like terms involves only constants, while collecting like terms involves only variables.

• Combining like terms is done before collecting like terms.

• There is no significant difference; the terms are interchangeable.

What is the recommended strategy for organizing terms when solving an equation with variables on both sides?

• Place all variable terms on one side and all constant terms on the other side of the equation.

• Place all terms on the left side of the equation.

• Place all terms on the right side of the equation.

• Keep variables and constants mixed on both sides until the final step.

Why does the instructor prefer to collect variable terms on the side with the larger coefficient?

• To make the equation more complex

• To avoid ending up with negative coefficients

• To simplify adding constants

• To avoid decimals

In the example equation 7x = 4x + 15, what operation is performed first to collect variable terms on one side?

• Adding 4x to both sides

• Subtracting 4x from both sides

• Dividing both sides by 7

• Adding 15 to both sides

When solving the equation 7x = 4x + 15, which side is recommended for collecting variable terms to avoid negative coefficients?

• The left side (where 7x is).

• The right side (where 4x is).

• It does not matter which side is chosen.

• Variable terms should not be collected on one side.

Solve the equation 5x - 2 = 3x + 4.

• x = 1

• x = 2

• x = 3

• x = 4

When solving this equation, 9n − 5 = 5n + 6, what do you think would be the first step? **Keep in mind we will always move all variable terms to the left of the equal sign

• subtract the 5n to the left

• subtract the 5 to the right

• add the 5n to the left

• subtract the 6 to the left

What do you do if a constant term appears on the same side as the variable terms?

• Leave it there and solve anyway

• Move it to the other side by adding or subtracting

• Multiply it by the variable coefficient

• Divide it by the number of terms

Why is it important to perform the same operation on both sides of the equation?

• To keep the equation balanced

• To make the numbers smaller

• To get rid of variables

• To combine constants