Solve Equation with Fraction or Decimal Coefficients. In the following exercises, solve each equation by...

Consider the equation,
${\displaystyle \frac{3}{4}a-\frac{1}{3}=\frac{1}{2}a+\frac{5}{6}}$
In order to find the solution follow the steps given below:
First find the least common denominator of all the fractions.
Then, multiply both sides of the equation by the least common denominator.
Then, use Distributive Property which states that for any real numbers a, b and c, ${\displaystyle a(b+c)=ab+ac}$.
Then simplify.
The least common denominator is 12.
So, ${\displaystyle 12(\frac{3}{4}a-\frac{1}{3})=12(\frac{1}{2}a+\frac{5}{6})}$
${\displaystyle 12\left(\frac{3}{4}a\right)-12\left(\frac{1}{3}\right)=12\left(\frac{1}{2}a\right)+12\left(\frac{5}{6}\right)}$
${\displaystyle 9a-4=6a+10}$
${\displaystyle 9a-4-6a+4=6a+10-6a+4}$
Solve further to get,
${\displaystyle 3a=14}$
${\displaystyle \frac{3a}{3}=\frac{14}{3}}$
${\displaystyle a=\frac{14}{3}}$
Hence, ${\displaystyle a=\frac{14}{3}}$ is the solution of ${\displaystyle \frac{3}{4}a-\frac{1}{3}=\frac{1}{2}a+\frac{5}{6}}$.