Question
Solve for \( u \). \[ \frac{5}{4}=\frac{u+2}{6} \] Simplify your answer as much as possible.
Ask by Ruiz Rogers. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( u = \frac{11}{2} \)
Solution
To solve for u in the equation
(5/4) = (u + 2)/6,
start by multiplying both sides by 6 to eliminate the fraction on the right:
6 * (5/4) = u + 2
Calculate 6*(5/4):
(6*5)/4 = 30/4 = 15/2
Now the equation becomes:
u + 2 = 15/2
Subtract 2 from both sides to solve for u:
u = 15/2 - 2
Express 2 as 4/2 to have a common denominator:
u = 15/2 - 4/2 = (15 - 4)/2 = 11/2
Thus, the solution is:
u = 11/2
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Simplify this solution Beyond the Answer
To solve for \( u \) in the equation \[ \frac{5}{4}=\frac{u+2}{6}, \] we can start by cross-multiplying to eliminate the fractions. This gives us: \[ 5 \cdot 6 = 4 \cdot (u + 2). \] Calculating the left side: \[ 30 = 4(u + 2). \] Next, distribute the \( 4 \) on the right side: \[ 30 = 4u + 8. \] Now, to isolate \( 4u \), subtract \( 8 \) from both sides: \[ 30 - 8 = 4u. \] This simplifies to: \[ 22 = 4u. \] Finally, divide both sides by \( 4 \) to solve for \( u \): \[ u = \frac{22}{4} = \frac{11}{2}. \] Thus, the solution is \[ u = \frac{11}{2}. \]
