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Answer
\( a=20 \)
Solution
Solve the equation \( \frac{a}{2}=14-\frac{a}{5} \).
Solve the equation by following steps:
- step0: Solve for \(a\):
\(\frac{a}{2}=14-\frac{a}{5}\)
- step1: Multiply both sides of the equation by LCD:
\(\frac{a}{2}\times 10=\left(14-\frac{a}{5}\right)\times 10\)
- step2: Simplify the equation:
\(5a=140-2a\)
- step3: Move the variable to the left side:
\(5a+2a=140\)
- step4: Add the terms:
\(7a=140\)
- step5: Divide both sides:
\(\frac{7a}{7}=\frac{140}{7}\)
- step6: Divide the numbers:
\(a=20\)
The solution to the equation \( \frac{a}{2}=14-\frac{a}{5} \) is \( a=20 \).
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Simplify this solution Mind Expander
To solve the equation \( \frac{a}{2}=14-\frac{a}{5} \), first, we find a common denominator for the fractions involved. In this case, the least common multiple of 2 and 5 is 10. Rewriting the equation using the common denominator gives us: \[ \frac{5a}{10} = 14 - \frac{2a}{10} \] Now, we can eliminate the fractions by multiplying through by 10: \[ 5a = 140 - 2a \] Next, we will add \( 2a \) to both sides: \[ 5a + 2a = 140 \] \[ 7a = 140 \] To find \( a \), divide both sides by 7: \[ a = 20 \] Thus, the value of \( a \) is 20.
