ALEKS: Solving a multi-step equation given in fractional form

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Great video! Solving multi-step equations with fractions can be challenging, but you explained it well. I appreciate your step-by-step approach to solving the given problem. I have a few additional insights and clarifications to enhance the understanding for viewers.

First and foremost, when dealing with equations involving fractions, it's crucial to eliminate the fraction component by multiplying both sides of the equation by the least common denominator (LCD). In this case, the LCD is 2. By multiplying both sides by 2, you correctly eliminate the fraction on the right side. However, it's important to emphasize that we need to distribute the multiplication across all the terms on both sides of the equation. For instance, the left side becomes 2 * 5, which equals 10. On the right side, the 2 in the denominator cancels out with the 2 in the numerator, leaving us with (2 * 3x) + (2 * 19).

Next, during the process of isolating the 3x term, you accurately subtracted 19 from both sides of the equation, resulting in -9 on the left side. However, on the right side, it's essential to remember that the terms (3x + 19) - 19 do not cancel out completely. The subtraction should yield 3x, as the 19 term disappears, leaving only the 3x term on the right side.

Finally, when solving for x by dividing both sides of the equation by 3, you correctly obtained the solution x = -3. It's important to emphasize that the solution should be written as "x = -3" to indicate the value of x. This notation helps to avoid confusion and clearly communicates the result.

In addition, I commend your suggestion to plug the obtained solution back into the original equation to verify its correctness. By substituting x = -3 into the original equation, we can confirm that both sides of the equation are equal, ensuring the accuracy of our solution.

Overall, your explanation was clear and concise, and the solution you arrived at is correct. Your video serves as a helpful resource for individuals learning to solve multi-step equations with fractions. Keep up the excellent work, and I look forward to more math tutorials from you!



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