Solving Equations and Integer Properties

The video tutorial covers solving various math problems, including rational equations, negative exponents, prime factorization, and properties of consecutive integers. It demonstrates techniques such as finding common denominators, simplifying expressions, and using prime factorization to solve problems. The tutorial also emphasizes the importance of understanding the properties of numbers and algebraic manipulation.

What is the first step in solving the equation 1/x - 1/(x+1) = 1/(x+4)?

• Add 1 to both sides

• Multiply both sides by x

• Find a common denominator

• Invert both sides of the equation

When dealing with negative exponents, what is the equivalent expression for 1/2 to the power of -3?

• 2 to the power of 3

• 8

• 1/2 to the power of 3

• 1/8

What should you do first when you see negative exponents in an expression?

• Add the exponents

• Invert the numbers

• Subtract the exponents

• Multiply the exponents

In the problem involving beads, what is the significance of the number 147,000?

• It is the number of red beads

• It is the total number of beads

• It is the number of yellow beads

• It is the product of the point values of the removed beads

How many red beads were removed if the product of the point values is 147,000?

• 1

• 2

• 3

• 4

What is the value of y if 2/(1 + 2/y) = 1?

• 2

• 4

• 1

• 3

In the equation 2/(1 + 2/y) = 1, what is the first step to isolate y?

• Add 1 to both sides

• Multiply both sides by (1 + 2/y)

• Multiply both sides by y

• Subtract 1 from both sides

If a, b, and c are consecutive positive integers, which statement is always true?

• a + b + c is odd

• abc is even

• abc is odd

• a + b + c is a prime number

For consecutive integers a, b, and c, what is the result of (a + b + c)/3?

• Always an even number

• Always a prime number

• Always a fraction

• Always an integer

If a, b, and c are consecutive integers, what is the difference between c and a?

• 4

• 3

• 2

• 1