Solving Linear Equations Steps

The video tutorial explains how to solve a complex equation by simplifying it into a linear form. The instructor begins by introducing the equation and discussing its initial complexity. The process involves multiplying both sides to eliminate the denominator, simplifying the equation, and then solving for the variable x. The final solution is x = -10/19, and viewers are encouraged to validate the solution by substituting it back into the original equation.

What is the initial form of the equation presented in the video?

• 14x - 4 over 3x + 2 = 8

• 14x + 4 over negative 3x minus 2 = 8

• 14x + 4 over 3x - 2 = 8

• 14x + 4 = 8

What is the first step taken to simplify the equation?

• Subtract 4 from both sides

• Multiply both sides by negative 3x minus 2

• Add 3x to both sides

• Divide both sides by 8

What is the purpose of multiplying both sides by negative 3x minus 2?

• To eliminate the numerator

• To eliminate the denominator

• To simplify the numerator

• To simplify the equation

After eliminating the denominator, what operation is performed next?

• Add 24x to both sides

• Distribute 8 across negative 3x minus 2

• Subtract 4 from both sides

• Combine like terms

What is the result of distributing 8 across negative 3x minus 2?

• -24x + 16

• 24x - 16

• 24x + 16

• -24x - 16

How are the x terms combined on the left-hand side?

• By dividing 14x by 24x

• By multiplying 14x by 24x

• By subtracting 24x from 14x

• By adding 14x and 24x

What is the equation after combining like terms?

• 38x = -16

• 38x + 4 = -16

• 38x = -20

• 38x - 4 = -20

What is the final step to solve for x?

• Subtract 4 from both sides

• Divide both sides by 38

• Add 4 to both sides

• Multiply both sides by 38

What is the simplified form of x?

• -10/19

• -20/38

• -5/19

• -10/38

What should you do to verify the solution?

• Substitute x back into the original equation

• Multiply x by 2

• Add 10 to x

• Check if x satisfies a different equation