Solving Linear Equations and Word Problems

The video tutorial begins with an introduction and two warm-up problems, followed by detailed solutions to two algebraic equations. The instructor explains each step, including distributing terms, combining like terms, and solving for variables. The session concludes with a word problem involving a number trick, demonstrating the application of algebraic concepts in real-world scenarios.

What is the first step suggested for solving the equation 3x - 1 = 2x + 3?

• Multiply both sides by 2

• Distribute the coefficients

• Add 1 to both sides

• Subtract 3 from both sides

After distributing the coefficients in the equation 3x - 1 = 2x + 3, what is the next step?

• Multiply both sides by 3

• Subtract 2x from both sides

• Divide both sides by x

• Add 3 to both sides

In the equation z/16 = 2(3z + 1)/9, what operation is performed first to simplify the equation?

• Divide both sides by 16

• Subtract 2 from both sides

• Multiply both sides by 9

• Add 9 to both sides

What is the result of distributing the 2 in the equation z/16 = 2(3z + 1)/9?

• 9z + 2

• 6z + 2

• 3z + 1

• 2z + 3

What is the main goal when solving the equation z/16 = 2(3z + 1)/9?

• To find the value of x

• To isolate z on one side

• To eliminate fractions

• To simplify to a quadratic equation

In the word problem, what operation does Tomar suggest first?

• Add 5 to the number

• Multiply the number by 5

• Subtract 3 from the number

• Divide the number by 3

What is the final step in Manoj's method for the word problem?

• Subtract 3 from the result

• Multiply the result by 3

• Add 5 to the result

• Divide the result by 2

What equation is set up to solve the word problem involving Andrew's number?

• 5x + 3 = 3(x + 5)

• 3x - 5 = 5(x + 3)

• 5x - 3 = 3(x + 5)

• 3x + 5 = 5(x - 3)

What is the value of x that satisfies both Tomar and Manoj's methods?

• 7

• 10

• 9

• 8

What is the final result Andrew gets using both methods in the word problem?

• 54

• 48

• 42

• 36