Solving Linear Equations and Transformations

In this video, Mr. Boskin guides students through a series of math problems, including comparing cell phone plans, solving biking speed problems, matching stories to equations, and evaluating the truth of equations. The video also covers solving algebraic equations and describing rigid transformations in geometry.

If Plan A costs $70 per month with a free $500 phone, and Plan B costs $50 per month without a phone, how many months will it take for the total cost of Plan B to equal Plan A if you buy a $500 phone?

• 25 months

• 10 months

• 15 months

• 20 months

Han rides at 16 miles per hour. How far does he travel in t hours?

• 16 + t miles

• 16t miles

• t/16 miles

• t + 16 miles

Priya starts biking half an hour before Han. If Han has been biking for t hours, how long has Priya been biking?

• t hours

• t - 0.5 hours

• 2t hours

• t + 0.5 hours

Which story matches the equation: -6 + 3x = 2 + 4x?

• A card game where players earn points for matching cards.

• A race between two cars with different speeds.

• A savings account with different interest rates.

• Two weather stations with temperatures changing at a constant rate.

For what value of x do the expressions (2/3)x + 2 and (4/3)x - 6 have the same value?

• x = 14

• x = 12

• x = 10

• x = 8

Decide whether the equation 2x = -3.5x is true for all, one, or no values of x.

• All values

• One value

• Cannot be determined

• No values

Solve the equation: 9x - 18 = 7x + 5.

• x = 2

• x = -2

• x = -1

• x = 1

What is the solution to the equation: -2(5 - 3d) = 3d + 16?

• d = 8

• d = 26/3

• d = 5

• d = 3

Describe the transformation that takes polygon A to polygon B.

• Dilation by a factor of 2

• Reflection over the x-axis

• Rotation 180 degrees around the origin

• Translation by 5 units right

What is the value of k in the equation: 5k - 12 = 3k + 4?

• k = 4

• k = 12

• k = 16

• k = 8