Solving Linear Equations with Fractions

The video tutorial explains how to solve an equation involving fractions by eliminating the fractions through multiplication. The instructor demonstrates the process of simplifying the equation, isolating the variable x, and solving for its value. The solution is verified by substituting it back into the original equation to ensure both sides are equal. The tutorial emphasizes the importance of understanding the least common multiple and the distribution of multiplication across terms.

What is the initial equation presented in the video?

• 3/8x - 2 = 3/4x + 4

• 3/4x + 2 = 3/8x - 4

• 3/4x - 2 = 3/8x + 4

• 3/8x + 2 = 3/4x - 4

Why is it beneficial to eliminate fractions when solving the equation?

• It makes the equation longer.

• It simplifies the equation.

• It makes the equation more complex.

• It introduces more variables.

What number is used to eliminate the fractions in the equation?

• 4

• 6

• 8

• 10

What is the result of multiplying 8 by 3/4x?

• 7x

• 5x

• 4x

• 6x

After eliminating fractions, what is the simplified form of the equation?

• 6x - 16 = 3x - 32

• 6x + 16 = 3x + 32

• 6x - 16 = 3x + 32

• 6x + 16 = 3x - 32

What operation is performed to move 3x from the right side of the equation?

• Divide both sides by 3x

• Add 3x to both sides

• Subtract 3x from both sides

• Multiply both sides by 3x

What is the value of x after solving the equation?

• -16

• -12

• -10

• -8

How is the solution verified in the video?

• By checking with a calculator

• By substituting x back into the original equation

• By graphing the equation

• By solving a different equation

What is the result of substituting x = -16 into the original equation?

• Both sides equal -12

• Both sides equal -10

• Both sides equal -8

• Both sides equal -6

What is the purpose of multiplying each term by the same number when solving equations?

• To introduce new terms

• To change the equation

• To eliminate variables

• To maintain equality