Problem 21 - Prealgebra

Question

Solve each equation. Check your solution. $$n-4.72=7.52$$

Step-by-Step Solution

Answer

The solution is \(n = 12.24\).

Step 1: Understanding the Equation

Our objective is to find the value of \(n\) in the equation \(n - 4.72 = 7.52\). The equation states that 4.72 subtracted from \(n\) gives us 7.52.

Step 2: Isolate the Variable

To isolate \(n\), we need to remove 4.72 from the left-hand side. To do this, add 4.72 to both sides of the equation: \(n - 4.72 + 4.72 = 7.52 + 4.72\).

Step 3: Simplifying the Equation

Adding 4.72 to -4.72 results in 0, so \(n + 0 = 7.52 + 4.72\). Simplifying further, we find \(n = 12.24\).

Step 4: Verify the Solution

Substitute \(n = 12.24\) back into the original equation to check: \(12.24 - 4.72 = 7.52\). Calculate the left side to confirm: \(12.24 - 4.72 = 7.52\), which matches the right side of the equation, verifying that our solution is correct.

Key Concepts

Solving Equations

When you encounter an equation like \(n - 4.72 = 7.52\), your goal is to find out what number \(n\) represents. This process is known as 'solving equations.' It involves performing operations to both sides of the equation that will eventually isolate the variable— in this case, \(n\).
One of the core principles is what we do to one side of the equation, we must do to the other to maintain balance. This balance is key to ensuring that the equality holds true at every step of solving the equation.

Checking Solutions

Once you've found a potential solution to the equation, like \(n = 12.24\), the next important step is to verify that solution. This involves substituting the value of \(n\) back into the original equation to see if it holds true.
For our equation, inserting \(12.24\) gives \(12.24 - 4.72 = 7.52\). Simplifying the left-hand side results in \(7.52\), which matches the right-hand side, confirming our solution. This step of 'checking solutions' confirms that the value found is indeed correct and maintains the balance of the initial equation.

Isolate Variables

Isolating the variable is an essential step in solving equations. In our example equation \(n - 4.72 = 7.52\), we need to get \(n\) by itself to find its value.
To do this, you should perform the opposite mathematical operation to remove any numbers attached to the variable. In this process, since \(-4.72\) is subtracted from \(n\), we add \(4.72\) to both sides of the equation. This cancels the \(-4.72\) on the left side, leaving us with \(n = 12.24\).
Remember, isolating the variable means reconfiguring the equation so the variable stands alone on one side of the equation. This method is crucial to finding the unknown value accurately.