Verified Answer :

  • Move the variable terms to one side of the equation by subtracting \(2.6a\) from both sides: \(2.7a - 7.9 = 2.9\).
  • Isolate the variable term by adding \(7.9\) to both sides: \(2.7a = 10.8\).
  • Solve for \(a\) by dividing both sides by \(2.7\): \(a = 4\).
  • The final answer is \(\boxed{4}\).

Explanation

  1. Problem Analysis and Strategy

The equation to be solved is \(5.3a - 7.9 = 2.6a + 2.9\). This is a linear equation in one variable, \(a\). To find the value of \(a\), we need to isolate the variable term on one side of the equation and the constant terms on the other.

  1. Collecting Variable Terms

To group the terms containing \(a\), we subtract \(2.6a\) from both sides of the equation:
\[5.3a - 2.6a - 7.9 = 2.9\]
Simplifying the expression on the left side gives:
\[2.7a - 7.9 = 2.9\]

  1. Isolating the Variable Term

Now, to isolate the term with \(a\), we add \(7.9\) to both sides of the equation:
\[2.7a = 2.9 + 7.9\]
Calculating the sum on the right side:
\[2.7a = 10.8\]

  1. Solving for \(a\)}],example_of_usage:

Finally, we solve for \(a\) by dividing both sides of the equation by \(2.7\):
\[a = \frac{10.8}{2.7}\]
Performing the division:
\[a = 4\]
Thus, the value of \(a\) is \(4\).

Examples

Linear equations are frequently used in budgeting and financial planning. For instance, if a service provider charges a base fee plus a rate per hour, you can model your total cost as a linear equation. Solving this helps you determine how many hours you can afford within a specific budget. Similarly, this algebraic approach is essential in fields like physics for calculating motion or in chemistry for determining concentration levels when mixing substances. Understanding these steps allows you to solve for any unknown variable efficiently in a real-world scenario.

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