Verified Answer :

  • Start with the original equation \(501 = 578 - 3x\).
  • Move the terms to isolate \(3x\) by rewriting the equation as \(3x = 578 - 501\).
  • Simplify the subtraction to get \(3x = 77\).
  • Divide by 3 to find the exact value \(x = \frac{77}{3}\).
  • Final Answer: \(\boxed{\frac{77}{3}}\)

Explanation

  1. Analysis of the Equation

We are given the linear equation \(501 = 578 - 3x\), where \(x\) is the unknown variable. Our goal is to isolate \(x\) to find its value. The equation involves a constant term, a variable term, and a constant on the other side, which requires basic algebraic rearrangement.

  1. Isolating the Variable Term

To isolate the term involving \(x\), we can move \(3x\) to the left side and \(501\) to the right side of the equation. Adding \(3x\) to both sides gives:
\[3x + 501 = 578\]
Subtracting 501 from both sides, we get:
\[3x = 578 - 501\]

  1. Calculating the Final Value of x

Now, calculate the difference on the right side:
\[578 - 501 = 77\]
So the equation becomes:
\[3x = 77\]
Dividing both sides by 3 to solve for \(x\):
\[x = \frac{77}{3}\]
This can also be written as a mixed number or decimal, \(x = 25 \frac{2}{3}\) or approximately \(x \approx 25.67\). The exact value is \(\boxed{\frac{77}{3}}\).

Examples

Linear equations are fundamental in everyday planning, such as budgeting. For example, if you have a budget of \$578 to spend and you must reserve \$501 for essential expenses, you can determine how many items costing \$3 each (let this be \(x\)) you can afford with the remaining money. By solving \(501 + 3x = 578\), you find exactly how many units you can purchase while staying within your total budget.

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