Verified Answer :

  • Subtract 3 from both sides to get \(-2x = -18\).
  • Divide by \(-2\) to isolate \(x\).
  • The solution is \(x = \boxed{9}\).

Explanation

  1. Analysis of the Equation

The problem asks to solve the linear equation \(-2x + 3 = -15\) for the variable \(x\). This is an algebraic equation of the form \(ax + b = c\), where \(a = -2\), \(b = 3\), and \(c = -15\). To find the value of \(x\), we need to isolate it on one side of the equation. We can do this by first removing the constant term from the left side and then dividing by the coefficient of \(x\).

  1. Isolating the Variable Term

To isolate the term involving \(x\), we subtract 3 from both sides of the equation:
\[-2x + 3 - 3 = -15 - 3\]
Simplifying both sides gives:
\[-2x = -18\]

  1. Solving for x and Verification

Now, we isolate \(x\) by dividing both sides of the equation by \(-2\):
\[x = \frac{-18}{-2}\]
Calculating the quotient:
\[x = 9\]
Thus, the value that makes the equation true is \(x = 9\). We can verify this by substituting \(x = 9\) back into the original equation: \(-2(9) + 3 = -18 + 3 = -15\), which confirms the result.

Examples

Solving linear equations is essential in everyday budgeting. For instance, if you have a budget of \(\$15\) to spend on a taxi ride where there is a fixed boarding fee of \(\$3\) and a variable cost of \(\$2\) per mile, the equation \(-2x + 3 = -15\) could represent the balance remaining. While this specific equation is abstract, similar structures allow you to determine how many units of a resource you can afford or calculate unknown quantities in balanced systems. Mastering these steps ensures you can solve for any unknown variable in linear relationships.

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