Questions: Use the multiplication principle to solve the following equation. Don't forget to check. 14/5 = -35 s

Solution Steps

To solve the equation \(\frac{14}{5} = -35s\) using the multiplication principle, we need to isolate the variable \(s\). This can be done by multiplying both sides of the equation by the reciprocal of the coefficient of \(s\), which is \(-35\). After finding the value of \(s\), we should substitute it back into the original equation to verify the solution.

We start with the equation: \[ \frac{14}{5} = -35s \] To isolate \(s\), we multiply both sides by the reciprocal of \(-35\): \[ s = \frac{\frac{14}{5}}{-35} \]

Now we simplify the expression for \(s\): \[ s = \frac{14}{5} \cdot \frac{1}{-35} = \frac{14}{-175} = -\frac{2}{25} \] Thus, we find: \[ s = -0.08 \]

To verify, we substitute \(s = -0.08\) back into the original equation: \[ -35s = -35(-0.08) = 2.8 \] Now we check if: \[ \frac{14}{5} = 2.8 \] Calculating \(\frac{14}{5}\): \[ \frac{14}{5} = 2.8 \] Since both sides are equal, the solution is verified.

Final Answer