Question
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Tutor-Verified Answer
Answer
\( q=\frac{5}{18} \) or \( q=0.2\dot{7} \)
Solution
Solve the equation \( q+\frac{5}{9}=\frac{5}{6} \).
Solve the equation by following steps:
- step0: Solve for \(q\):
\(q+\frac{5}{9}=\frac{5}{6}\)
- step1: Move the constant to the right side:
\(q=\frac{5}{6}-\frac{5}{9}\)
- step2: Subtract the numbers:
\(q=\frac{5}{18}\)
The solution to the equation \( q+\frac{5}{9}=\frac{5}{6} \) is \( q=\frac{5}{18} \) or \( q=0.2\dot{7} \).
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Simplify this solution The Deep Dive
To solve for \( q \) in the equation \( q + \frac{5}{9} = \frac{5}{6} \), start by isolating \( q \). You can do this by subtracting \( \frac{5}{9} \) from both sides: \[ q = \frac{5}{6} - \frac{5}{9} \] Next, you'll need a common denominator to subtract the fractions. The least common multiple of 6 and 9 is 18. Convert both fractions: \[ \frac{5}{6} = \frac{15}{18} \quad \text{and} \quad \frac{5}{9} = \frac{10}{18} \] Now, substitute these back into the equation: \[ q = \frac{15}{18} - \frac{10}{18} = \frac{5}{18} \] So, the solution is: \[ \boxed{\frac{5}{18}} \]
