Verified Answer :

  • Combine the \(x\) terms on the left side: \(1x + 0.15x = 1.15x\).
  • Rewrite the equation as: \(1.15x = 3.45\).
  • Divide both sides by 1.15 to isolate \(x\): \(x = \frac{3.45}{1.15}\).
  • The solution is \(\boxed{3}\).

Explanation

  1. Problem Analysis

We are given the linear equation:
\[x + 0.15x = 3.45\]
Our objective is to solve for the variable \(x\). The equation represents a situation where we add a portion (15%) of a quantity to the quantity itself to reach a total value of 3.45. This can be viewed as combining like terms on the left side of the equation.

  1. Simplifying the Equation

To solve the equation \(x + 0.15x = 3.45\), we combine the terms containing \(x\). The term \(x\) can be written as \(1x\). Thus, adding \(1x\) and \(0.15x\) gives:
\[(1 + 0.15)x = 3.45\]
\[1.15x = 3.45\]
This simplifies the equation significantly, allowing us to isolate \(x\) by performing a single division operation.

  1. Solving for x

To isolate \(x\), we divide both sides of the equation by 1.15:
\[x = \frac{3.45}{1.15}\]
Performing the division:
\[x = 3\]
Thus, the value that satisfies the given equation is 3.

Examples

Imagine you are buying a product that has a 15% sales tax. If the total price you paid at the register is \$3.45, you can use this equation to find the original price of the item before tax. If \(x\) is the original price, then the total cost is the original price plus 15% of that price, written as \(x + 0.15x = 3.45\). Solving this gives the original price of \(\$3\). Understanding how to solve these types of equations is essential for budgeting, understanding taxes, and calculating discounts or interest.

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