Verified Answer :

  • Isolate the variable term by adding 8 to both sides: \(\frac{h}{4} = 21\).
  • Multiply both sides by 4 to solve for the variable: \(h = 21 \times 4\).
  • The final value for the variable is \(\boxed{84}\).

Explanation

  1. Analyzing the Equation

The problem requires solving the linear equation \(-8 + \frac{h}{4} = 13\) for the variable \(h\). We need to isolate \(h\) on one side of the equation by performing inverse operations. First, we observe that the term \(\frac{h}{4}\) is affected by the constant \(-8\). To eliminate \(-8\), we add \(8\) to both sides of the equation.

  1. Isolating the Variable Term

Starting with the equation:
\[-8 + \frac{h}{4} = 13\]
Adding \(8\) to both sides yields:
\[-8 + 8 + \frac{h}{4} = 13 + 8\]
\[\frac{h}{4} = 21\]

  1. Solving for h

Now, we have \(\frac{h}{4} = 21\). To solve for \(h\), we multiply both sides of the equation by \(4\):
\[\frac{h}{4} \times 4 = 21 \times 4\]
\[h = 84\]
Thus, the solution is \(h = 84\).

Examples

Linear equations like this are common in everyday life, such as calculating budget adjustments. For example, if you start with an initial debt of \(\$8\) and you want to reach a target of \(\$13\) in your bank account, you might perform a series of transactions where a quarter of a deposit (let's say \(h/4\)) brings you to that goal. Solving this equation helps you determine exactly how much the total deposit \(h\) needs to be to achieve your financial target.

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