Solving Linear Equations with Variables in the Denominator

The video tutorial explains how to solve the equation 7 - 10/x = 2 + 15/x. It begins by identifying the issue of x in the denominators and suggests multiplying both sides by x to simplify the equation. The tutorial then demonstrates distributing x and simplifying both sides to form a linear equation. The process of solving the linear equation by isolating x is shown, followed by verifying the solution by substituting it back into the original equation.

What is the initial equation presented in the video?

• 7x - 10 = 2x + 15

• 7 + 10/x = 2 - 15/x

• 7x + 10 = 2x - 15

• 7 - 10/x = 2 + 15/x

What is the first step to simplify the equation with x in the denominator?

• Add x to both sides

• Multiply both sides by x

• Subtract x from both sides

• Divide both sides by x

After multiplying both sides by x, what does the left-hand side of the equation become?

• 7x + 10

• 7x - 10

• 7 + 10x

• 7 - 10x

What is the right-hand side of the equation after distributing x?

• 2 - 15x

• 2 + 15x

• 2x - 15

• 2x + 15

What is the next step after simplifying the equation to 7x - 10 = 2x + 15?

• Subtract 10 from both sides

• Add 10 to both sides

• Subtract 2x from both sides

• Add 2x to both sides

What is the equation after subtracting 2x from both sides?

• 5x - 10 = -15

• 5x - 10 = 15

• 5x + 10 = 15

• 5x + 10 = -15

How do you isolate x in the equation 5x - 10 = 15?

• Add 10 to both sides

• Subtract 10 from both sides

• Multiply both sides by 5

• Divide both sides by 5

What is the value of x after solving the equation?

• x = 5

• x = 3

• x = 4

• x = 6

What is the purpose of substituting x back into the original equation?

• To verify the solution

• To find a new solution

• To simplify the equation further

• To eliminate x from the equation

What is the result when substituting x = 5 back into the original equation?

• 5 = 7

• 5 = 6

• 5 = 4

• 5 = 5