Answer
The solution is $a = \frac{4}{5}$.
To check our answers, we plug the values into the original equation.
$5 + \frac{7}{\frac{4}{5}} = \frac{11}{\frac{4}{5}}$
Multiply to simplify:
$5 + \frac{35}{4} = \frac{55}{4}$
Convert $5$ into a fraction with $4$ as its denominator:
$\frac{20}{4} + \frac{35}{4} = \frac{55}{4}$
Add:
$\frac{55}{4} = \frac{55}{4}$
This solution is correct.
Work Step by Step
The first thing we want to do is get rid of the fractions. We do this by multiplying both sides by the denominator(s) of the fraction(s) we want to eliminate:
$5a + 7 = 11$
Collect constants on the right side of the equation:
$5a = 4$
Divide both sides by $5$:
$a = \frac{4}{5}$
The solution is $a = \frac{4}{5}$.
To check our answers, we plug the values into the original equation.
$5 + \frac{7}{\frac{4}{5}} = \frac{11}{\frac{4}{5}}$
Multiply to simplify:
$5 + \frac{35}{4} = \frac{55}{4}$
Convert $5$ into a fraction with $4$ as its denominator:
$\frac{20}{4} + \frac{35}{4} = \frac{55}{4}$
Add:
$\frac{55}{4} = \frac{55}{4}$
This solution is correct.
