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a) \( \frac{a}{2}=14-\frac{a}{5} \)

Ask by Ortega Ruiz. in South Africa
Feb 19,2025

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\( a=20 \)

Solución

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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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.

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