Exploring Adding and Subtracting Rational Expressions

What is the fundamental rule when solving algebraic equations?

• Only perform operations on one side of the equation.

• Ignore operations on the right side of the equation.

• Operations are not necessary on both sides.

• Perform the same operation on both sides of the equation.

What property of equality is used when you add the same value to both sides of an equation?

• Subtraction property

• Division property

• Multiplication property

• Addition property

If you subtract a number from one side of an equation, what must you do to maintain balance?

• Multiply the number on the other side

• Subtract the number from the other side

• Add the number to the other side

• No action needed on the other side

What results from dividing both sides of an equation by the same non-zero number?

• The equation becomes unbalanced

• The equation remains balanced

• The operation is generally not allowed

• Only the left side of the equation changes

In the equation 'X + 4 = 9', what operation would you use to solve for X?

• Division

• Multiplication

• Addition

• Subtraction

How do you solve the equation '-6X = 42' for X?

• Add 6 to both sides

• Subtract 6 from both sides

• Multiply both sides by -6

• Divide both sides by -6

What is the result of multiplying both sides of an equation by the same number?

• The equation becomes invalid

• The equation becomes simpler

• The equation's variables disappear

• The equation remains balanced

In the context of division, why can't you divide by zero?

• It results in an undefined operation

• It makes the equation too complex

• It simplifies the equation too much

• It balances the equation perfectly

What does the division property of equality allow you to do?

• Divide both sides of an equation by the same non-zero number

• Multiply both sides of an equation by a number

• Subtract a number from both sides of an equation

• Add a number to both sides of an equation

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

• To simplify the equation

• To maintain the balance of the equation

• To solve the equation faster

• To make the equation more complex