Solving Linear Equations Involving Rationals

What is the first step in simplifying an equation with variables in the denominator?

• Divide both sides by the highest coefficient

• Subtract the denominators from both sides

• Multiply both sides by the least common denominator

• Add the denominators together

What does cross multiplication involve in solving equations?

• Subtracting terms from opposite sides

• Dividing one side by the other

• Multiplying diagonally opposite terms

• Adding cross terms from both sides

After applying cross multiplication, what is the next step to isolate the variable 'x'?

• Divide by the coefficient of x

• Distribute and combine like terms

• Multiply through by x

• Add all constants to one side

What is the purpose of distributing terms in an equation?

• To isolate the variable on one side

• To simplify the equation's denominators

• To prepare the equation for addition

• To combine like terms

Why can't cross multiplication be used directly in the new problem introduced?

• Because the equation does not contain any variables

• Because the denominators are already simplified

• Because there are multiple fractions on one side

• Because there is no fraction in the equation

What is the correct method to clear off denominators in the new problem?

• Divide each term by the common denominator

• Multiply each term by the common denominator

• Multiply through by the sum of denominators

• Subtract the denominator from both sides

What is the result of simplifying the equation after removing the denominators?

• No variables remaining in the equation

• A constant value on both sides

• A single variable on one side

• An equation with variables on both sides

How do you verify that a solution to an equation with denominators is valid?

• Make sure the solution equals one of the denominators

• Check that the solution is a whole number

• Ensure the solution does not make any denominator zero

• Confirm the solution is positive

What happens if a solution results in a zero in the denominator?

• The solution is automatically zero

• The solution needs to be recalculated

• The solution is undefined and invalid

• The solution is considered valid

What is the final step in solving for 'x' after all transformations?

• Divide by the coefficient of 'x'

• Subtract all constants from 'x'

• Add all constants to the left side

• Isolate 'x' on one side of the equation