Question

and counting! fantastic consistency.
solve for j.
$-\frac{1}{3} = \frac{j}{4} - \frac{10}{3}$

Explanation:

Step1: Add $\frac{10}{3}$ to both sides

To isolate the term with \( j \), we add \(\frac{10}{3}\) to both sides of the equation \(-\frac{1}{3}=\frac{j}{4}-\frac{10}{3}\).
\[
-\frac{1}{3}+\frac{10}{3}=\frac{j}{4}-\frac{10}{3}+\frac{10}{3}
\]
Simplifying the left - hand side: \(-\frac{1}{3}+\frac{10}{3}=\frac{- 1 + 10}{3}=\frac{9}{3} = 3\).
The right - hand side simplifies to \(\frac{j}{4}\) (since \(-\frac{10}{3}+\frac{10}{3}=0\)). So now we have the equation \(3=\frac{j}{4}\).

Step2: Multiply both sides by 4

To solve for \( j \), we multiply both sides of the equation \(3=\frac{j}{4}\) by 4.
\[
3\times4=\frac{j}{4}\times4
\]
Simplifying both sides: The left - hand side is \(12\), and the right - hand side is \(j\) (since \(\frac{j}{4}\times4 = j\)).

Answer:

\(j = 12\)