Problem 48 - Algebra A Combined Function

Question

Solve. $$ m+2=7.1 $$

Step-by-Step Solution

Answer

m = 5.1

Step 1: Isolate the Variable

To solve the equation \( m + 2 = 7.1 \), we need to isolate the variable \( m \). The goal is to have \( m \) on one side of the equation. To do this, subtract 2 from both sides of the equation.

Step 2: Perform Subtraction

Subtract 2 from both sides of the equation: \( m + 2 - 2 = 7.1 - 2 \). This simplifies to \( m = 5.1 \).

Step 3: Verify the Solution

Check your work by substituting \( m = 5.1 \) back into the original equation: \( 5.1 + 2 = 7.1 \). The equation holds true, verifying that the solution is correct.

Key Concepts

Isolation of Variables

Imagine you're a detective and you need to uncover the secret identity of a variable. In the context of solving equations, "isolation of variables" is all about getting the variable you are trying to solve for (in this case, "m") all by itself on one side of the equation. Start with balancing both sides of the equation. If there's something added to your variable, like in this equation where 2 is added to "m", you'll do the opposite operation to remove it. Here, subtracting 2 from both sides allows the equation to show clearly what "m" equals:

• Original Equation: \( m + 2 = 7.1 \)
• Subtract 2 from both sides: \( m = 7.1 - 2 \)
• Result: \( m = 5.1 \)

Always apply the same operation to both sides of the equation to maintain balance. This process is useful in ensuring that only the variable you are solving for remains on one side.

Verification of Solutions

Checking your work is as crucial in math as in any detective's work. After solving for a variable, like finding \( m = 5.1 \), you need to verify your solution to confirm it is correct. This means substituting your solution back into the original equation to see if both sides are equal. For \( m + 2 = 7.1 \):

• Substitute \( m = 5.1 \) back into the equation.
• Calculate \( 5.1 + 2 \).
• If it equals \( 7.1 \), then your solution is verified!

Verification is vital because it confirms the solution is not only possible, but also correct. This practice helps in avoiding calculation errors and ensures that you have arrived at the right conclusion.

Simplifying Equations

Equations are like puzzles. Simplifying them makes it easier to see the solution. Simple equations are more straightforward to solve and less confusing to work with. In our exercise example, \( m + 2 = 7.1 \), there's not much to simplify beyond handling the operation directly. However, in more complex equations:

• Combine like terms when possible.
• Simplify fractions, if present.
• Address any operations involving parentheses by applying distribution.

These steps make equations less complicated, leading to efficient and quick solutions. Simplifying is the act of using fundamental operations to make the equation’s structure as basic as possible, sometimes before isolating the variable or verifying the solution.