91Ó°ÊÓ

When solving linear equations, the first crucial step is to isolate the variable. This simply means getting the variable on one side of the equation by itself. To do this, you must remove or simplify other terms that are attached to it. In the given exercise, we have the equation:\[5m + 7 = -13\]
To isolate the variable "m," you need to eliminate the constant term, which in this case is 7.

• Subtract 7 from both sides: \(5m + 7 - 7 = -13 - 7\)
• This results in the equation: \(5m = -20\)

Now that "m" is alone on one side, this process sets you up to easily solve for the variable. It’s important to perform the same operation on both sides of the equation to keep it balanced.Doing this correctly is key to ensuring the variable is properly isolated, paving the way for finding its value.

Once you find the value of the variable, it's important to check your solution. This step confirms that your answer satisfies the original equation.For our equation, after isolating the variable, we found that \(m = -4\). To verify this is correct, substitute \(m = -4\) back into the original equation:\[5(-4) + 7 = -13\]
Calculate step-by-step:

• Multiply: \(5 \times -4 = -20\)
• Add: \(-20 + 7 = -13\)

Since both sides of the equation equal \(-13\), we see that our solution of \(m = -4\) satisfies the equation. This step is crucial because it provides reassurance that no mistakes were made during calculations or manipulations.

Verification in solving equations is a bit like double-checking your work. It's not just about getting an answer; it's about ensuring it’s the right one. To verify that \(m = -4\) is indeed the correct solution, it's critical to review each step of the solution process:

• Ensure that each algebraic operation (like adding, subtracting, multiplying, or dividing) was correctly applied.
• Check if the operations were consistently performed on both sides of the equation to maintain balance.

Revisiting the calculations and logical steps allows any overlooked errors to surface. Verification makes sure that understanding is solid, and reinforces the reliability of your answer.Through verifying the given problem, confidence in both your solution and method is built, which is an essential practice in mastering algebra.