Question

solve for u.
-\frac{1}{3} - \frac{1}{2}u = \frac{3}{5}
simplify your answer as much as possible.
u = \square

Explanation:

Step1: Add $\frac{1}{3}$ to both sides

To isolate the term with \( u \), we add \(\frac{1}{3}\) to both sides of the equation \(-\frac{1}{3}-\frac{1}{2}u = \frac{3}{5}\). This gives us:

$$ -\frac{1}{2}u=\frac{3}{5}+\frac{1}{3} $$

First, find a common denominator for the right - hand side. The common denominator of 5 and 3 is 15. So, \(\frac{3}{5}=\frac{3\times3}{5\times3}=\frac{9}{15}\) and \(\frac{1}{3}=\frac{1\times5}{3\times5}=\frac{5}{15}\). Then \(\frac{3}{5}+\frac{1}{3}=\frac{9 + 5}{15}=\frac{14}{15}\). So the equation becomes \(-\frac{1}{2}u=\frac{14}{15}\).

Step2: Solve for \( u \)

Multiply both sides of the equation \(-\frac{1}{2}u=\frac{14}{15}\) by \(- 2\) to solve for \( u \). When we multiply both sides by \(-2\), we have:

$$ u=\frac{14}{15}\times(-2)=-\frac{28}{15} $$

Answer:

\(u = -\frac{28}{15}\)