Summary
Learn how to solve a multi-step linear equation that initially contains variables in the denominator. This video demonstrates simplifying the equation by multiplying by 'x' and then using standard algebraic techniques to isolate the variable.
Highlights
Introduction to the Equation and Initial Challenge
00:00:00
The video introduces the equation 7 - 10/x = 2 + 15/x and challenges viewers to solve it. The main difficulty lies with the 'x' in the denominators.
Eliminating the Denominators
00:00:34
To simplify the equation, both sides are multiplied by 'x'. Distributing 'x' on the left side results in 7x - 10, and on the right side, it becomes 2x + 15. This transforms the equation into a standard linear form.
Solving the Linear Equation
00:01:28
The goal is to move all 'x' terms to one side. Subtracting 2x from both sides gives 5x - 10 = 15. Then, adding 10 to both sides results in 5x = 25. Finally, dividing by 5 yields x = 5.
Verification of the Solution
00:02:44
The solution x = 5 is verified by substituting it back into the original equation. This results in 7 - 10/5 = 2 + 15/5, which simplifies to 7 - 2 = 2 + 3, or 5 = 5, confirming the solution is correct.