Verified Answer :

  • To solve the equation \(24 - 8x = -16\), subtract \(24\) from both sides to obtain \(-8x = -40\).
  • Divide both sides by \(-8\) to isolate \(x\).
  • Calculate the result: \(x = 5\).
  • Final Answer: \(\boxed{5}\)

Explanation

  1. Problem Analysis

The problem asks us to solve for \(x\) in the linear equation \(24 - 8x = -16\). Our goal is to isolate \(x\) on one side of the equation to find its value. A linear equation represents a straight-line relationship, and solving it involves basic algebraic manipulation, specifically using the additive and multiplicative inverses to isolate the variable.

  1. Isolating the Variable Term

Start by isolating the term containing \(x\). Subtract \(24\) from both sides of the equation to move the constant term to the right-hand side:
\[24 - 8x - 24 = -16 - 24\]
This simplifies to:
\[-8x = -40\]

  1. Solving for x and Verification

Now, to solve for \(x\), divide both sides of the equation by \(-8\):
\[x = \frac{-40}{-8}\]
Dividing a negative number by a negative number results in a positive number:
\[x = 5\]
We can verify this result by substituting \(x = 5\) back into the original equation:
\[24 - 8(5) = 24 - 40 = -16\]
Since this matches the original right-hand side, the solution is correct.

Examples

Imagine you have a budget of \$24 to spend on notebooks for your school project, and each notebook costs \$8. If you have a debt of \$16 that you need to pay off using the leftover money, you can use the equation @@MATH_TOKEN_20@@ to determine how many notebooks you bought that resulted in a remaining balance of -\$16. By solving this equation, you find that you purchased \(x = 5\) notebooks. This simple algebraic modeling helps you track your finances effectively.

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