Solving Linear Equations and Inequalities

The video tutorial covers solving algebraic equations by simplifying and identifying errors. It includes problems on simplifying expressions, solving for unknowns, and applying these skills to real-world scenarios like calculating rental costs and determining rope lengths. The tutorial emphasizes understanding each step in the process and correcting mistakes.

What is the equivalent equation after simplifying 5x - 2(7x + 1) = 14x?

• 9x - 2 = 14x

• -9x - 2 = 14x

• 5x - 14x = 14x

• 5x + 14x = 14x

What is the result of distributing the minus sign in the expression 5x - 2(7x + 1)?

• 5x + 14x + 2

• 5x - 14x - 2

• 5x - 14x + 2

• 5x + 14x - 2

When simplifying 4(2 - 5x) = 6 - 3(1 - 3x), what should be done first?

• Combine like terms

• Add 6 to both sides

• Distribute the 4 and 3

• Subtract 5x from both sides

In the equation 4(2 - 5x) = 6 - 3(1 - 3x), what is the simplified form of the right side after distribution?

• 6 + 3 + 9x

• 6 + 3 - 9x

• 6 - 3 - 9x

• 6 - 3 + 9x

What is the value of n if the total cost of renting a sailboat is $360, given by the equation 360 = 120 + 60n?

• 5 days

• 2 days

• 3 days

• 4 days

How many days was the sailboat rented if the equation is 360 = 120 + 60n?

• 3 days

• 2 days

• 1 day

• 4 days

In solving 3(x + 5) = 2x + 35, what was the first incorrect step?

• Combining like terms incorrectly

• Adding 5 to both sides

• Subtracting 2x from both sides

• Distributing 3 to both terms inside the parentheses

What is the correct simplification of 3(x + 5) = 2x + 35 after distributing the 3?

• 3x + 5 = 2x + 35

• 3x + 15 = 2x + 35

• 3x + 15 = 35

• 3x + 5 = 35

If a 120-foot rope is cut into three pieces where the first is twice the second and the third is three times the second, what is the length of the longest piece?

• 80 feet

• 60 feet

• 40 feet

• 20 feet

If the second piece of rope is x, what is the equation to find the total length of the rope?

• 2x + 3x = 120

• x + 2x + 3x = 120

• x + 3x = 120

• x + 2x = 120