Answer:
1/15 or 0.0666.. repeating
Step-by-step explanation:
1. Group all a terms on the left side of the equation
Add a to both sides
[tex]46a+\frac{5}{3}+a=\frac{24}{5}-a+a[/tex]
Group like terms:
[tex]46a+a+\frac{5}{3}=\frac{24}{5}-a+a[/tex]
Simplify the arithmetic:
[tex]47a+\frac{5}{3}=\frac{24}{5}-a+a[/tex]
Group like terms:
[tex]47a+\frac{5}{3}=-a+a+\frac{24}{5}[/tex]
Simplify the arithmetic:
[tex]47a+\frac{5}{3}=\frac{24}{5}[/tex]
2. Group all constants on the right side of the equation
[tex]47a+\frac{5}{3}=\frac{24}{5}[/tex]
Subtract [tex]\frac{5}{3}[/tex] from both sides:
[tex]47a+\frac{5}{3}-\frac{5}{3}=\frac{24}{5}-\frac{5}{3}[/tex]
Combine the fractions:
[tex]47a+\frac{5-5}{3}=\frac{24}{5}-\frac{5}{3}[/tex]
Combine the numerators:
[tex]47a+\frac{0}{3}=\frac{24}{5}-\frac{5}{3}[/tex]
Reduce the zero numerator:
[tex]47a+0=\frac{24}{5}-\frac{5}{3}[/tex]
Simplify the arithmetic:
[tex]47a=\frac{24}{5}-\frac{5}{3}[/tex]
Find the lowest common denominator:
[tex]47a=\frac{24\cdot 3}{5\cdot 3}+\frac{-5\cdot 5}{3\cdot 5}[/tex]
Multiply the denominators:
[tex]47a=\frac{24\cdot 3}{15}+\frac{-5\cdot 5}{15}[/tex]
Multiply the numerators:
[tex]47a=\frac{72}{15}+\frac{-25}{15}[/tex]
Combine the fractions:
[tex]47a=\frac{72-25}{15}[/tex]
Combine the numerators:
[tex]47a=\frac{47}{15}[/tex]
3. Isolate the a
[tex]47a=\frac{47}{15}[/tex]
Divide both sides by 47:
[tex]\frac{47a}{47}=\frac{\frac{47}{15}}{47}[/tex]
Simplify the division:
[tex]a=\frac{47}{15\cdot 47}[/tex]
Simplify the right side:
[tex]a=\frac{1}{15}[/tex]
hope this helps:)
