Verified Answer :

  • Identify the linear equation \(8 = -\frac{3}{4} t\).
  • Multiply both sides by the reciprocal of the coefficient \(-\frac{3}{4}\), which is \(-\frac{4}{3}\).
  • Simplify the resulting expression \(t = 8 \times -\frac{4}{3}\) to find the final value.
  • The final value is \(\boxed{-\frac{32}{3}}\).

Explanation

  1. Problem Analysis

We are given the linear equation \(8 = -\frac{3}{4} t\). Our goal is to isolate the variable \(t\) to find its value. This is a standard algebraic problem where we use the properties of equality to solve for an unknown.

  1. Solving the Equation

To isolate \(t\), we need to eliminate the coefficient \(-\frac{3}{4}\). We can do this by multiplying both sides of the equation by the reciprocal of the coefficient, which is \(-\frac{4}{3}\).
Performing this operation on both sides:
\[8 \times \left(-\frac{4}{3}\right) = \left(-\frac{3}{4} t\right) \times \left(-\frac{4}{3}\right)\]
This simplifies to:
\[-\frac{32}{3} = t\]
Thus, the value of \(t\) is \(-\frac{32}{3}\).

Examples

In physics, equations like this often appear when calculating displacement or acceleration. For example, if an object has a velocity of \(-8\) meters per second, and you are calculating the time \(t\) it takes to reach a certain position under a specific rate of change, simple linear equations allow you to find exactly how long or how far something traveled. Mastering these calculations is fundamental for understanding motion and change in any physical system.

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