Solving Proportions and Rational Equations

The video tutorial explains how to determine the least common denominator (LCD) by multiplying denominators and factoring them if possible. It demonstrates multiplying expressions by the LCD to eliminate fractions and solve rational expressions. The tutorial also covers applying the distributive property to solve equations, emphasizing the importance of getting variables on the same side.

What is the first step in determining the LCD?

• Divide the denominators

• Add the denominators

• Multiply the denominators

• Subtract the denominators

Why is it important to factor the denominators before finding the LCD?

• To make the problem more complex

• To find common terms

• To simplify the numerators

• To change the denominators

What should you do after finding the LCD?

• Multiply each expression by the LCD

• Add the LCD to each term

• Subtract the LCD from each term

• Divide the LCD by each term

What is the purpose of multiplying by the LCD?

• To eliminate the fractions

• To add more fractions

• To change the numerators

• To simplify the LCD

What property is applied after multiplying by the LCD?

• Identity property

• Distributive property

• Associative property

• Commutative property

What is the result of applying the distributive property to 8x - 4 = 10x + 30?

• 8x - 4 = 10x + 30

• 8x - 4 = 10x - 30

• 8x + 4 = 10x - 30

• 8x + 4 = 10x + 30

What is the next step after applying the distributive property?

• Divide both sides by 8x

• Multiply both sides by 8x

• Subtract 8x from both sides

• Add 8x to both sides

Why is it important to get the x's on the same side?

• To simplify the equation

• To make the equation more complex

• To change the denominators

• To add more fractions

What should you do after subtracting 30 from both sides?

• Add 30 to both sides

• Multiply both sides by 30

• Simplify the equation

• Divide both sides by 30

What is the final value of x in the equation?

• x = 34

• x = -34

• x = 17

• x = -17