Algebraic Problem Solving Techniques

This video tutorial covers solving linear equations with one variable, using real-world examples such as budgeting for kayak rentals, solving consecutive integer problems, mixture problems, ticket pricing with discounts, and work and time problems. Various methods for solving these equations are demonstrated, emphasizing the importance of setting up equations correctly and understanding the underlying concepts.

What is the main focus of Algebra 1 Lesson 1-2?

• Factoring polynomials

• Solving quadratic equations

• Solving linear equations

• Graphing linear equations

If Joshua has $50, how many hours can he rent a single kayak at $15 per hour?

• 3 hours

• 5 hours

• 4 hours

• 2 hours

How does the non-refundable equipment fee affect Joshua's kayak rental budget?

• It increases the total budget

• It decreases the amount available for hourly rental

• It has no effect on the budget

• It doubles the rental cost

What is a key difference between solving equations in parts A and B?

• Part A requires addition, Part B requires subtraction

• Part A requires division, Part B requires subtraction and division

• Part A requires subtraction, Part B requires multiplication

• Part A requires multiplication, Part B requires division

In solving the equation 2(x + 4)/3 - 8 = 32, what is the first step in Method 1?

• Add 8 to both sides

• Multiply each side by 3

• Divide each side by 2

• Subtract 4 from both sides

What is the value of x in the equation 4 + x(3x - 1)/2 = 9?

• 7

• 9

• 5

• 11/3

What are the three consecutive integers whose sum is 132?

• 44, 45, 46

• 43, 44, 45

• 42, 43, 44

• 45, 46, 47

How many liters of 10% acid solution are needed to make 25 liters of 15% acid solution?

• 10 liters

• 15 liters

• 20 liters

• 18.75 liters

What was the original price of one concert ticket before the discount?

• $95

• $85

• $90

• $93

Can Latonya be home in one hour if she walks to the bike shop and rides back?

• No, unless she reduces her waiting time

• Yes, she can be home in one hour

• Yes, if she increases her walking speed

• No, it will take her more than one hour