Solving Equations and Simplifying Expressions

The video tutorial explains how to solve an equation for the variable 'a'. It begins by introducing the equation and the concept of clearing fractions by multiplying both sides by the least common denominator. The tutorial then demonstrates distributing terms and isolating the variable 'a'. It concludes with simplifying the expression and exploring alternative forms of the solution, emphasizing the equivalence of different expressions.

What is the first step in solving an equation that contains a fraction?

• Divide both sides by the same number

• Add the same number to both sides

• Multiply both sides by the least common denominator

• Subtract the same number from both sides

When multiplying both sides of an equation by 'C', what happens to the fraction?

• It becomes larger

• It remains the same

• It is cleared

• It becomes a decimal

What are the two options for solving the equation after clearing the fraction?

• Multiplying or dividing

• Factoring or expanding

• Adding or subtracting

• Distributing or dividing

What is the purpose of distributing in the equation-solving process?

• To simplify the fraction

• To add more terms

• To change the variable

• To clear the parentheses

How do you isolate the 'a' term in the equation 3a + 3B = BC?

• Multiply both sides by 3

• Subtract 3B from both sides

• Divide both sides by B

• Add 3B to both sides

What is the final step to solve for 'a' in the equation 3a = BC - 3B?

• Add 3 to both sides

• Divide both sides by 3

• Subtract 3 from both sides

• Multiply both sides by 3

How can the expression (BC - 3B) / 3 be rewritten?

• BC / 3 - B

• BC / 3 + B

• B - BC / 3

• 3B / BC

Why is it important to recognize the equivalence of different forms of an expression?

• To change the variable

• To understand different ways of simplifying

• To confuse the reader

• To make the expression longer

What does dividing each term in the numerator by the denominator achieve?

• It makes the expression more complex

• It adds more terms

• It simplifies the expression

• It changes the variable

What is the equivalent expression for BC / 3 - B?

• BC / 3 + B

• 3B - BC

• BC + 3B

• (BC - 3B) / 3