Solving Equations: Did Vishnal Get It Right?

Hey math enthusiasts! Let's dive into a common algebra problem and see if our friend Vishnal nailed it. We're going to break down his steps and figure out if he solved the equation correctly. This is a super important skill, so pay close attention, guys!

The Equation and Vishnal's Steps

Alright, here's the equation we're looking at:

Line 1: $-7 - 2m = -9$

Vishnal's steps to solve it are as follows:

Line 2: $-2m - 7 = -9 + 7 + 7$

Line 3: $\frac{-2m}{-2} = \frac{-2}{-2}$

Line 4: $m = 1$

So, the big question is: Did Vishnal get the right answer? Let's meticulously examine his approach, line by line, to see if his reasoning and calculations hold up. Understanding how to solve such equations is fundamental in algebra, forming the basis for more complex problem-solving. This exploration will not only help us assess Vishnal's work but also reinforce our own understanding of equation manipulation. We will focus on the principles of isolating the variable and maintaining the equality throughout the process. It's like a balancing act; any operation performed on one side must be mirrored on the other to keep things fair. This process ensures that we arrive at the correct solution and accurately interpret the results. Through this analysis, we can identify common mistakes and strategies for solving equations effectively. Pay attention, as we will explain why each step matters and how it influences the final answer. Ready? Let's do this!

Breaking Down Vishnal's Solution

Let's meticulously check Vishnal's work, step by step, to find out if he solved the equation correctly. We will highlight any discrepancies and ensure that we understand each action's implication. It's all about making sure the math checks out! Understanding how equations work is crucial, so let's break it down.

Line 1: The Starting Point

The equation begins with $-7 - 2m = -9$. This is our starting point. We need to find the value of m that makes this equation true. Nothing wrong here; this line is perfect. It sets up the problem, and there's nothing to criticize.

Line 2: The First Move

Here's where things get interesting. Vishnal rewrote the equation. The equation should be to add 7 on both sides $-2m - 7 + 7 = -9 + 7$. However, Vishnal made a mistake in this step. He added 7 to both sides, which is the correct operation to move the constant term. But he did it wrong by adding 7 twice on the right side. This step should be to add 7 on both sides. In this line, he added 7 to both sides. Correctly. So, the equation should have been $-2m - 7 + 7 = -9 + 7$. This is not correct. We must keep in mind the order of operations when handling algebraic expressions. This step is about isolating the term containing m. Let's try to understand how Vishnal handled the equation, step by step. This is a critical step, and the accuracy here will determine whether we arrive at the correct solution. Remember, maintaining the balance of the equation is key. What Vishnal did here changed the original equation, which is not what we want to do when solving an equation.

Line 3: Isolating m

Line 3 is all about getting m by itself. We want to isolate m on one side of the equation. In this case, Vishnal divided both sides by -2. When we divide both sides by -2, we can arrive at the right answer. The correct method should have been dividing both sides by -2 to get the value of m. The goal is to make the coefficient of m equal to 1. This step is a direct consequence of the previous step. Any mistake made previously will carry over here, influencing the outcome. Correctly done, the equation looks like this: $\frac{-2m}{-2} = \frac{2}{-2}$. Note the original equation in line 2 should have been $-2m = -2$.

Line 4: The Final Answer

Here, Vishnal concludes that m equals 1. If he did the previous steps correctly, then this should have been the final solution. This is where we see if all the previous steps led to the correct solution for m. Given the error in line 2, his final answer is not correct. To ensure we have found the correct value for m, we can substitute the value back into the initial equation. If the equation holds true, then our answer is accurate. So, let's substitute m = 1 into the original equation $-7 - 2m = -9$. This yields $-7 - 2(1) = -9$. Simplify: $-7 - 2 = -9$, which simplifies to $-9 = -9$. This implies that Vishnal's answer is correct only if the intermediate steps were done correctly, which in this case, they were not.

The Verdict: Did Vishnal Get It Right?

Based on our step-by-step analysis, unfortunately, Vishnal did not solve the equation correctly. The main issue lies in the way Vishnal set up line 2. The proper approach involves isolating the term containing m. He incorrectly rewrote and manipulated the equation in the initial steps, leading to an incorrect result. That's why the answer he provided is incorrect. It's a classic example of how a small mistake early on can lead to a wrong answer, highlighting the importance of precision in every step of solving an equation. It's not about memorizing formulas; it's about understanding what's happening at each step. Always double-check your work, guys!

What Vishnal Should Have Done

So, what's the correct way to solve this equation? Let's take a look at the right approach:

1. Start with the original equation: $-7 - 2m = -9$
2. Add 7 to both sides: $-7 - 2m + 7 = -9 + 7$, simplifying to $-2m = -2$
3. Divide both sides by -2: $\frac{-2m}{-2} = \frac{-2}{-2}$, simplifying to $m = 1$

This would have been the correct way to solve for m. Remember, always double-check your work!

Key Takeaways and Tips for Solving Equations

• Isolate the variable: Your main goal is to get the variable (in this case, m) by itself on one side of the equation.
• Maintain balance: Whatever you do to one side of the equation, you MUST do to the other side. This is crucial for keeping the equation true.
• Check your work: Always substitute your answer back into the original equation to ensure it's correct. This helps catch any calculation errors.
• Practice makes perfect: The more you solve equations, the better you'll become at recognizing patterns and avoiding mistakes. Do lots of practice problems.

By following these tips and understanding the steps involved, you'll be well on your way to mastering algebraic equations. Keep practicing, and don't be afraid to ask for help! Equations might seem tricky at first, but with practice, they become much easier to solve. Always remember the fundamental principles, and you'll be able to solve most equations without a problem. Good luck, and keep up the great work!