Inequalities, Ratios, and Exponents

The video tutorial covers solving various mathematical problems, including equations with fractions, calculating vehicle accidents using ratios, determining swim team members through percentages, finding the number of managers using ratios, solving quadratic equations, and solving inequalities. Each problem is broken down step-by-step, demonstrating different mathematical techniques and logical reasoning.

What is the value of x if 1 + 1/x = 2 - 2/x?

• x = 4

• x = 3

• x = 2

• x = 1

If 96 vehicles out of 100 million are involved in accidents, how many vehicles are involved in accidents out of 3 billion?

• 2,880

• 2,880,000

• 288,000

• 28,800

What is the result of simplifying the expression 10^9 / 10^8?

• 100

• 1000

• 1

• 10

What is the total number of members in a swim club if 30% have passed a test and 70% equals 42 members?

• 42

• 60

• 50

• 70

In a company, the ratio of managers to workers is 5:72. If 8 more workers are hired, the ratio becomes 5:74. How many managers are there?

• 15

• 10

• 20

• 25

If (x - 1)^2 = 400, what could be the value of x - 1?

• 20

• -20

• Neither

• Both 20 and -20

What is the value of x if x - 1 = 20?

• x = 19

• x = 20

• x = 22

• x = 21

What is the value of x if x - 1 = -20?

• x = -21

• x = -19

• x = -18

• x = -20

Which of the following describes all values of x for which 1 - x^2 is greater than or equal to 0?

• x < 1

• x > -1

• -1 ≤ x ≤ 1

• x = 0

If x^2 ≤ 1, which of the following is true?

• x is between -1 and 1

• x is always negative

• x is greater than 1

• x is always positive