QuestionAugust 25, 2025

Solve for u. (5)/(4)u-(1)/(2)=-(4)/(3) Simplify your answer as s much as possible. u=- square

Solve for u. (5)/(4)u-(1)/(2)=-(4)/(3) Simplify your answer as s much as possible. u=- square
Solve for u. (5)/(4)u-(1)/(2)=-(4)/(3) Simplify your answer as s much as possible. u=- square

Solution
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Answer

u = -\frac{2}{3} Explanation 1. Isolate the variable term Add \frac{1}{2} to both sides: \frac{5}{4}u = -\frac{4}{3} + \frac{1}{2}. 2. Simplify the right side Find a common denominator (6): -\frac{4}{3} = -\frac{8}{6} and \frac{1}{2} = \frac{3}{6}. So, -\frac{8}{6} + \frac{3}{6} = -\frac{5}{6}. 3. Solve for u Multiply both sides by \frac{4}{5} to isolate u: u = -\frac{5}{6} \times \frac{4}{5}. 4. Simplify the expression Calculate: u = -\frac{20}{30} = -\frac{2}{3}.

Explanation

1. Isolate the variable term<br /> Add $\frac{1}{2}$ to both sides: $\frac{5}{4}u = -\frac{4}{3} + \frac{1}{2}$.<br /><br />2. Simplify the right side<br /> Find a common denominator (6): $-\frac{4}{3} = -\frac{8}{6}$ and $\frac{1}{2} = \frac{3}{6}$. So, $-\frac{8}{6} + \frac{3}{6} = -\frac{5}{6}$.<br /><br />3. Solve for $u$<br /> Multiply both sides by $\frac{4}{5}$ to isolate $u$: $u = -\frac{5}{6} \times \frac{4}{5}$.<br /><br />4. Simplify the expression<br /> Calculate: $u = -\frac{20}{30} = -\frac{2}{3}$.
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